Changing PhD Programs? What to put in my application? (UK-based) Background: 
I started my PhD a few months ago. I haven't actually been trained to do anything because they say they don't have the time for it. I've been understanding but I'm becoming very frustrated. In addition, it looks like my project might not work out at all and some other P.I. advised my supervisor to change the direction of my PhD completely. I've come up with a few ideas I could do in the meanwhile but most of them have been rejected. I feel helpless. I have voiced my concerns to my supervisor but nothing has changed. 

I am considering re-applying to other programs so I have other options if this situation remains the same. Ideally, I would like to submit my applications without my supervisor knowing. Is it possible, and more importantly is it a good idea? Furthermore, I know I have to disclose that I am currently doing a PhD but how much will this hurt my chances at applying to other places and how do I go about it? Do I just mention it in my CV or should I attach a letter explaining my situation, will anyone even read that? Do I still have a chance to get into another fully funded program? 

Sorry for the million questions. I would really appreciate if someone who's been or knows anyone in this situation could help me out. Thank you!
It looks like your question is a typical X-Y problem: you are frustrated with the uncertainty and lack of direction from your current supervisor (problem X), you want to solve this by applying to another PhD program, but you don't know how to present your current situation in the application (problem Y).

So let's take a step back: the best scenario for you is probably to solve problem X in your current institution. 
Here is what you can do to solve the problem with your current supervisor:


If there is any experienced academic around you that you trust, talk to them about your best course of action. Advice from a local person who knows the ins and outs of the department is often very useful.
Ask for a meeting with the local ombudsman or your director of studies. At this stage you don't need to tell your supervisor about this meeting and you can ask to talk to this person in confidence. Explain your issue with the supervisor to them and see what they have to say; in this kind of case various options can be considered:


A meeting with the supervisor and this person, where different options for the direction of your PhD are discussed clearly and openly, and you get to express your opinion about them.
Adding a co-supervisor more compatible with the kind of research you want to do and/or more available: this can be a good compromise if your supervisor is not interested in the topic you want to work on.   
A change of supervisor: if things really don't work out between you and this supervisor, it's usually possible to switch. This can be a bit more complicated, but it's still much better than quitting.



My advice is to think about re-applying somewhere else only if none of these solutions are satisfying or possible in your institution.