You're in a hard spot, a spot I know quite well. Just one thing it is important to remember in these situations is to not ascribe intentions to words that may not exist. I think for example that it is unfair to label his response to your question as immature. No doubt he genuinely does not know. He clearly loves you, and loves his children, and wants things to work out, but he is not sure if it is healthy for him to stay, either. That is HUGE decision to make, and he shouldn't answer one way or the other until he is sure.
I do not think you should push him to leave or cower from confrontation. I do think you should beg, barter or pay for a baby sitter to take the kids so the two of you can have some serious time to discuss what's going on.
Three weeks is too long to not talk.
When my DH and I went through something like this we discovered that the success of my career was a catalyst for a lot of self-loathing coming to the surface and it coincided with his 40th birthday which was pretty bad. He felt like I cared about everyone but him and the kids, that I was leaving him behind. He needed more autonomy. He needed to be needed in major ways. He needed his own life and friends. He needed to feel appreciated more obviously. I needed security which for me meant not feel a wave of resentment and anger every time I walked through the door. I needed acknowledgement that I was doing a good job as a wife and mother despite also being the sole breadwinner. I needed support to get the job done impressively enough that I would be up for promotion. Neither of us could meet the other's needs with the set up as it was. So we made childcare happen so Dh could go back to work doing what he loves rather than what he can to make our ends meet.
I don't know what it will be for your DH and you, but the important thing is to sit down and figure out what each of you NEEDS and then find out how together you can meet those needs. The CNVC has a lot of great techniques for getting to the bottom of bad feelings and finding out the unmet needs beneath. It really helps us to communicate less judgementally. So instead of saying "he's being so immature!" or "He's being really mean." I say "He's not speaking to me." then I think, what would make him not want to talk? Depression? Anxiety? Anger? Thoughtfulness? Reflection? and instead of assuming he is punishing me (which I would have before). Then when I ask him I don't say "What did I do to deserve this treatment!?" (even if what I said out loud is "what's wrong?" the tone of the accusation could be heard) I say "you seem upset. Do you want to talk about it?" and if the answer is no, I can trust he trusts me enough to tell me the truth. and then I can say "Will you let me know if there is anything I can do or if you want to talk about it?"
And if I have a need to talk to him I can say "I feel lonely and I need connection. I'd like to have that connection with you, to hear your voice. Will you talk to me about what's been going on with you?" It's an observation, a need, and an honest request. And if that is met with an honest denial, I meet that need elsewhere and do not hold his inability or unwillingness to meet my need against him or as a reflection of his love for me (well, that's the THEORY! ha ha old habits die hard, right?) It's a good practice of communication and it has really helped us to communicate better.