It sounds like your husband does literally nothing to help with the kids. You don’t need to apologise for not wanting sex. He should be apologising for not helping you! Admittedly I only have one kid, so my perspective might be different, but in my house, I am the one who does the 5.30 wake ups and early morning play, then I go off to work and I’m home to do bathtime and bedtime. Sharing the load makes a huge difference to both my and my wife’s mental health and feelings towards each other.