Is OTHER wrong in the post ? POST : Long time lurker but had to create a temporary account to post since others know the main one.

Background: I live with my parents and I asked if I could have a dog and they said as long as I can afford him and his necessities and take care of him, they wouldn't mind. They emphasized the many facts that they will not help me in any way (buying stuff, dog-sitting, training, etc) which I didn't mind, I have always wanted a furbaby and I wanted the responsibility of training him to be the best doggo ever.

The first few months was all great, I learned so much and implemented everything I've learned from dog training courses, videos online, advice from friends who have dogs, all that good stuff. Since my doggo is a fairly large breed, it is more difficult to address some issues. I've tried positive reinforcement all the way but it only went so far.. so my private trainer suggested to use a pinch collar. I was hesitant to use this but after a few training sessions with this, the obedience changed for the better and the issues gradually got easier to deal with such as tugging during walks. The trainer suggested not to let him play with other dogs yet since he is still trying to master obedience.

So after the 6 months mark, my parents grew to love the dog soo much that they started spoiling him like crazy when I am not present. My mom would give him treats non-stop cause he would give those cute freaking puppy eyes.. My mom calls me cold-hearted because I would ask the dog to do tricks (obedience training) before I give him a reward. I want to enforce the training so he is not spoiled and has to earn his treats even if the command is something simple like "sit" or "down". My parents also love to walk him, but they don't enforce the pinch collar during walks. So the dog is tugging left and right, he's leading them everywhere, he's eating crap off the ground, he's plopping on the ground and refusing to leave, etc. 

At this point, this dog KNOWS who and when he can take advantage of - he would basically revert back to the behavior prior the pinch collar if hes around my parents. My parents would complain to me, asking me why he's acting this way and why he's such an angel when he's with me. They would compare my dog to others asking why can't I train him to be obedient like other dogs. I told them bluntly that it is because they don't enforce the training, and that I do. They still didn't listen to me after I told them this fact. 

I found out that my mom has been letting him play with other dogs on walks, even after I told her not to yet since we are still trying to master obedience. She lets him off-leash and he goes running towards other dogs.. I told her that I don't like if the dog is off-leash unless it's in an enclosed area. What if the other dog he's running towards is aggressive? What if the other dog's owner doesn't like dogs being off-leash? She then continues to call me crazy, and that I am making the dog unhappy. One of the main reason that I am overly upset right now is because my mom told me that the dog saw other dogs from the other side of the park and he went running towards them- leading to the fall of my mom and letting go cause of severe leash burn. I've tolerated so much regarding about the dog but my mom just continues not to listen and tells me that I'm being a bad owner and that I don't care about his well-being. I got so fed up that I regretfully yelled at my mom and now she's crying.. and giving me the silent treatment. All my dog training literally went down the toilet.

Sorry for the long post, but AITA for yelling at mom because I just want her to enforce the training so he doesn't go all crazy and takes advantage of her? I know she just wants the dog to be happy.