Q:

How to handle people blocking your view and breaking the rules at the theater by not sitting in their assigned seats?

A while ago, my parents/brothers and I went to visit a theatre performance (in The Netherlands, where we live). We booked really nice first class tickets with empty seats in front of us. We booked them very last-minute, hoping we would be lucky, and we were. A few of the seats in front of us were still empty during the performance. After the break, what looked like a mother and her daughter (in her early teens) entered the row in front of us, and stopped at the seats in front of me and my dad. 
I clearly overheard their talk, and the girl was telling her mother that these were not their seats, that their seats were about 5 rows further back. Her mother tried to keep up the act that these were their seats though. In the end, she noticed they now had our attention, and asked us 'Are these seats taken?'. 
Mom and dad were hesitating, so I just cut in: 

No, these seats aren't taken. And no, they will not be taken either. We booked our seats this way, so maybe no one would be in front of us. I clearly overheard your daughter telling you that you booked seats about five rows further back, so please go to the seats assigned to you on your ticket, or I will go and fetch an attendant to remind you where they are. 

Might be of interest that we booked 1st class tickets, and that about 2 rows further back, 2nd class started. So they were basically trying to get a free upgrade. Also note that taking seats that aren't assigned to you is breaking the theatre's house rules. 
Despite my answer, the mother sat down, and pulled the girl into a chair as well, the girl already looked majorly uncomfortable and embarassed at this point. So, I got up, didn't engage the mother further, fetched the nearest attendant like I had promised, and they came with me to remove them to their own seats. 
The girl's mother started insulting my mom, telling her she had done a poor job raising me, that the only thing she did right was feeding me (I am overweight, ouch). At this point, only the attendant's presence probably prevented this from escalating into a proper, physical fight. This ladies remarks managed to take away some of the good spirits we were in that evening, despite us all having had a really good time up to that moment, and us trying to dismiss/joke it off afterwards. We were all a bit less cheery for the rest of the evening.
While the attendant escorted mom and her daughter to their proper seats, 
I started feeling bad for the girl, she was looking so embarrassed with the way her mom was behaving, we were feeling less cheery but she was close to tears. 
I get the impression something in my response/actions triggered all of this, but I can't really put a finger on what it was. 
So, next time someone takes seating not assigned to them, how can I handle the situation in a way that won't make the other person feel a need to be nasty and ruin our cheerfulness, while at the same time prevent possible children of being embarassed by their parent's behavior?

There have been a lot of comments saying it's not 'my job to enforce the rules' or that these people were perfectly entitled to take those seats, so to clarify a bit further to avoid this confusion:
In the Netherlands, it's perfectly acceptable (and even expected) to point out to people that they're breaking a rule and inconveniencing you, before getting any authorities involved. People talking in a silence carriage, people smoking outside of smoking areas, people taking seats that aren't theirs to take, neighbors causing stench by having 30 dogs: It's expected you point out that there's rule they're breaking, that they're inconveniencing you, and only after go fetch an authority. 
So yeah, while it's technically not my job to 'enforce' the rules by physically moving these strangers to their proper seats, it's my 'job' (duty?) to tell them, when seeing people trying to take seats that aren't theirs, and being asked whether these seats are free, that these seats may be free but not theirs to take according to the rules of the theater, and to let them know breaking it will get them into trouble.
If they hadn't asked, and I had seen them commit the offense, I could've silently flagged an attendant or pointed out their mistake to them in a more gentle way, like 'Hey, we didn't see you here before the break, did you miss the beginning?'. But by asking whether the seats are free (which, as LordFarquaad pointed out in their answer is equal to confessing you're trying to commit an offense), the burden was up to us to tell them that they were trying to break the rules being fully aware of them (which is slightly worse than unknowingly breaking a rule). 
A lot of people might be thinking that I'm only taking offense to the seat being occupied, but the combination of them deliberately breaking the rules in combination with them not paying for the seats and limiting a view, all while engaging us in the process, is what makes it worthwhile enough to be assertive.

A:

I have been the kid in a situation like this. My father can behave a lot like this girl's mother. It is extremely embarrassing when your parents break social norms. 
Let's analyse their behaviour. One or more of them wanted better seats. One of them, most likely the mother decided to take the empty seats in front of you, which were an upgrade. The houserules of the theater and social etiquette don't allow that, but they did so anyway. It seems like the girl was more aware of the rules and/or social etiquette than the mother (or cared more for them). Being her parent, the mother is in a position of power over the girl. The mother forced the girl to do something embarrassing: breaking social norms. 
At that point they realised you caught them in the act of doing something embarrasing. What is even more embarrassing than doing something embarrassing? Being seen doing something embarrassing. At this point the mother asked "are these seats taken?". She was looking for confirmation from you that it was okay to sit there. 
Here's where an opportunity to stop them feeling embarrassed appeared. You could have said "no" and left it at that. You'd have confirmed that their actions are within social norms for you. That does not get you to your desired outcome, though. 
You could have said yes or some not-definite no, but that would be a white lie. You may not feel so good about lying, and they would know you lied when no one turned up in the end, but you would have saved them some embarrassment. 
You said

I clearly overheard your daughter telling you that you booked seats about five rows further back

At this point, you confirmed you caught them red-handed. This must have increased the embarrassment even further. But the mother continued the socially unacceptable behaviour and sat down.
Here, you could have used something less... accusatory. The part about getting an attendant can also be considered threatening (as pointed out by Imus). This gets their defences up. Perhaps

Those seats were supposed to be empty. We bought these more expensive seats for exactly that reason. Are you sure those seats are yours?

The question allows them to back off graciously, instead of even more embarrassed. The way you've described this mother, it may not work, though it should have achieved overall lower embarrassment levels. The high embarrassment levels are probably what fueled the mother's anger. Her intrapersonal issues are not your fault. 
Should they not go back to their seats at that point, you can escalate (peacefully). This does bring more embarrassment to them, but that is entirely on the mother. 
You got caught in a catch-22, set up by the mother. Suffer or embarrass. The only thing you can do is damage control. 

A:

I used to work in a cinema where this is a problem. 
You did the correct thing by getting the attendant and letting them deal with it, that is what they are trained to do.
The only thing I would potentially do in the future differently is not even engage them to begin with, generally if someone knows they are doing something wrong in a public setting like a theatre, they are much more likely to ignore you than accept defeat. 
When I noticed them sit in seats which they obviously were not supposed to be in, I would quietly grab a steward and they will do the rest. That will avoid a direct confrontation with yourself and will have the desired outcome of them being moved.  

A:

In any theater with assigned seating, it is not your job to remove people from seats they haven't paid for.  That is the job of the ushers and other staff, who are paid to check tickets and are (perhaps minimally) trained to resolve disputes.
If you know the seats are not taken, but you don't want to tell the person asking, instead defer: 

They may or may not be, why don't we ask the attendant?

If you are determined to thwart their intention to take the seats, add, 

Here, let me get the attendant for you.

and watch them quickly sidle away, knowing their tickets will be checked and they will be exposed.
Still, how hard would it have been to just let them have the seats, since no one was sitting there?  You could even become co-conspirators by telling them that you know the seats are available, and help to set the daughter's mind at ease. Yes, they're taking seats they didn't pay for, but they're not your seats and it's unlikely that they would have seriously impeded your view.  
This way, you all get to enjoy a better view of the performance, and walk away happy, instead of creating an entirely avoidable public squabble that left you all feeling upset.  I just don't see the upside.

