OP this is absolutely heartbreaking. I can feel your pain through your posts. I'm going to be blunt: your mum can get to fuck. The way she feels about keeping up appearances and that being gay is shameful is not shared by everyone. I won't pretend homophobia doesn't exist today – clearly, as your mum is demonstrating, it does – but there is absolutely nothing shameful about being gay, and I seriously doubt your friends would judge you if you came out and left your marriage. If they are true friends, they'd want to support you.
You've internalised so many messages that you don't matter, which is just so sad to read. You DO matter and you DO deserve to be happy – even if that is at the expense of someone else's happiness. The kids will adapt. Your husband – well, he'll just have to deal with it, won't he. Marriages and relationships break up all the time. I've been dumped before when I really didn't want the relationship to end, it was devastating, but I got over it and moved on because I had no choice. The person who wants to end the relationship gets the final say, because breaking up isn't a democracy.
I'd argue that even if you weren't gay it's not healthy for them to be around their father's homophobic attitudes. Are you concerned he might try and poison them again you if you left? That's a pretty good reason not to leave them with him, isn't it?
The only thing I'd think of someone in your position who left their marriage and came out, is how brave they were, and what a wonderful relief that they finally get to live their authentic life. I don't believe that other people's happiness should come before your own (or anyone's) even if it's kids –long term, the worst thing to do for kids is stay in an unhappy relationship. It'll really fuck up their ideas and behaviours around relationships when they're adults. Even if you think they're shielded from it, they pick things up subconsciously. Trust me, I know, I wish more than anything that my parents had divorced.
What I'm trying to say OP is that YOU MATTER. This is something I think you need to work on with your therapist, to start believing your needs can be prioritised and that you deserve to be happy.
Can you sort alternative childcare? It sounds like cutting your mum out of your life might be the first step to feeling better about yourself.