You've reached the right decision but in telling him, a world of hurt will follow and no-one deserves this. I'm afraid that given the extra info you have provided I would suggest, and I know this is difficult for you, that you let him go entirely, do not allow him to move out and still see him to "work on it"
The reality is that when one partner moves in with another who has kids, its not a proper partnership unless he is accepting family responsibilities. In no way, financially, emotionally or practically is he a family member. He is a lodger with physical benefits and servants so he has no right to dictate. He has no say in the family dynamics as he is simply the lodger and in fairness, as you are a mum, it concerns me that you allowed him to move in on this basis as its unfair to your family. But when we are in love and feel we are asking someone to take on a lot, we make compromises. You are way undervaluing yourself, you and your family are worth so much more.
Mother issues apart, any man that wants to be with you in a longterm relationship, takes on not just you but your family. Living with you means sharing the financial, emotio al and practical realities of family life. If your chosen partner cannot offer this up front (taking into account money limitations), then they should not be invited into your home.
This guy wants you on his terms without supporting your responsibilities and he is a freeloader. You deserve so much more and he will never step up to be the man you and your family need and you are a package deal.
You have been naive, but we have all done this and we just have to learn from it.
You have a horrendous task in front of you. My heart goes out to you. I would suggest you pack his stuff when he is out. That you ask mum to take the kids out and you deliver the news and tell him he needs to go immediately. He will say its unreasonable on many levels and he will gaslight you. Do not let him stay until he finds somewhere else, the problems he will cause during that time are not worth it and quite honestly you have already been too accommodating and he has taken the piss.
Make him leave, recover the keys, and this is why it must be a surprise to him, so he doesn't get them copied or budget to change the locks changed. Block him on all phones and social media as he will not go quietly. Tell him to write with his new address and you will forward his post for a couple of months until he has time to redirect. it. Do not give him any money or any promises to do so, you have subsidised him enough.
Tell your kids and mum that you made a mistake and he wasn't right for you and he had to go. This is not a case of him or your mum, its a case of him being controlling when he has no right to be and you and your family deserve better.
You come as a package deal and any man has to buy into the whole package or he is out. That doesn't mean that for the right man, there aren't reasonable adjustments to be made on all sides. This current guy is not accepting the whole package and I am not even covering your mum here, he wants cheap lodgings, no responsibility and to control everything, what a deal....can I move in please?
Be strong lady, you can do this, its ok to cry, rage and ask why this happens to you. And its ok to miss your special guy but realistically he isn't special in the right way and you can do better!
Big hugs and let us know the outcome.