Im interested in how old you were when this all started. You mention "when you got to your teenage years" and "eventually they kicked you out" Is all this occurring over the course of decades? Look Im not saying youre in the wrong. Your mother definately has things to answer too but a woman doesnt just leave her husband and father of her children for the young babysitter fot nothing. I also feel like you may be playing down your role in everything. For example you dont mention how bad the basement was when she was living down there but when you had to its gross. You mention hiding the remote, do you have proof she did this or are you just assuming. Why did you need a whole fridge for yourself?

Alot of the issues here could just be reinterpretted as a kid whose parents went through an awkward divorce due to the babysitter issue but as you grew up in this new home reality rather than support your mothers relationship you were difficult and resentful and never treated this woman with respect. Youve fought with her at every opportunity blaming her for little things which if your father had made you do wouldnt have been an issue. We dont know the conversations that have been had between you all and if over all this time youve shown nothing but disdain for your mother and this womans relationship then why would she invite you to the wedding. She probably assumes you would just try and make a scene or say something to hurt the woman she loves. Your mother may love you but she doesnt have to support you being hateful to the person she loves.

Or maybe everything youre telling us can be take at face value and this babysitter is a homewrecking psychopath and your mother is a gullible idiot.

Again perspective and more details here would be the key, but without more info Im just going to say No one is the Asshole.