I can't say what is going on in his brain, but as much as I love my kids as they do me, I thought about how hard it would be to try rebuilding any kind of life while being the 'one who left/was kicked out'. Having to pay for it just makes the resentment grow.
It doesn't change my love, but there were many dark days that I figured I was going to lose them anyhow - if not now, when they are older and have decided to hate me for leaving. I know they'll never really get the bad dynamics of my R with my W, but I assumed if they're going to hate me, maybe it would be best not to try and to move on quickly.
Now, I'm not sure if I'll be D or not by years end, but I came to grip with those feelings enough to present various options to my W that always kept the kids in both my and her lives. The laws here help; you can't even move out of city without consultation and possibly court appearances to ensure children under 16 always get their needs considered first.
Having a heart-to-heart, no guilt, talk with him might help. I'm on the alt (dbust) and if you want some articles that you could give him about why he should really consider being more involved. Involved doesn't mean calling, it means being in contact.
Finding out what he would like if a D goes through may be helpful, if you haven't already discussed that.
Some real hard 180s or decisions you could consider (remember, I'm just thinking...it's your life!) - Move closer to him so the kids don't have to lose their family members - Ask him to move closer to you for visitation - Offer him the house during weekend days for him to spend time with them - Find out if he would like to have the kids visit at his place
I guess what I'm saying is that a calm, kind & loving discussion in person (over coffee with a babysitter at home?) might make him wake up and pull his head up toward his children again.
BTW-My 3 yr old doesn't need any reason for a tantrum, so consider yourself lucky! The worst for me isn't the 3yr old either, it is the 10 year old. She gets the idea of separation so much more.