Sorry TC, I just feel sad about your situation. I understand some of your sentiments about keeping things right for the kids and whatnot. But my two cents- you need to create your own life now. That means moving out, finding your own space, a job, etc. If it means you have to take some charity from mom in the short term, so be it. But work towards your own independence, taking whatever time you need.
All while doing this, you don't have to damage anything with your kids, or do you have to make things ugly with your ex. Keep it civil. But you are married and have rights. You speak of a house that's only in her name- if this asset was acquired while you are married, barring any prenup agreements, you have some ownership there (generally 50/50 for all assets acquired while you were married), sure maybe you don't want to "take" the house, but this could maybe rights to some assistance on her part for you to find somewhere else to live.
Maybe you don't want to call it this, but she is the unfaithful party here. You didn't ask for the end of this relationship. But alas, its happening, and you need to recognize your own self worth. You have rights and ownership in things here. And asking for this isn't being petty or a jerk or something. You do need to get legal representation ASAP so you can claim what is owed to you as a result of this 10 year partnership that has yielded many children. If the wife wants to move on, so be it, but you don't need to be a doormat. You all can be civil and even friendly, but you do need to stick up for yourself.
You all can go on to be a functioning three person unit where your children are concerned, but you have the right to your own life, and to your own place to live- free of watching your ex "move on" day in and day out, and the right to form your own relationships away from them, while still being just as much of a parent to your children. Yes, the kids would have two homes and that sucks, but it happens all the time, and most come out of it just fine (and far better when they have two happy parents).
