Second to what Brandi said about the LDS moms thread - some of them may not see this here so you might get it moved and/or copy the thread into that sticky.
I'm so sorry you are going through this.

I haven't been in your shoes, so I can only imagine, but I am sure it's terribly hard to go without him every week.
I don't think he should worry what people will think about him being released. I mean, I never even know who holds what stake callings until stake conference twice a year, and even then, half the time I don't hear anything.
But it kind of sounds like that's an excuse for him, anyway, since he was making up reasons not to go in the first place.
It is nice that your in-laws are there.
Do they help out with trying to get him reactivated? I'm sorry to hear his mission was a negative experience for him.
I wonder if he had some issues before his mission, that were never resolved... just a thought.
As for scriptures and FHE - even if he won't take the lead - is he at least willing for you to do those things? If he isn't offended/upset about it, I would suggest you go ahead and take the lead on those things. Choose a time of day when you can read scriptures with your kids. For us, we do it at bedtime - each person reads one verse. We are barely out of Mosiah and we've been working on it for 2.5 years!

Slow & steady wins the race... For the ones who are too young to read, we read it to them in a whisper and they say it out loud. Same thing for family prayer. Maybe you can just do those things anyway.
I will say, I've known several women whose husbands were either non members or inactive members, and the good example of their righteous wives is what got them back into the church! One woman was married to nonmember for 50 YEARS! He was polite about the church and would even have the missionaries over to dinner but would never take the discussions. He finally got baptized and they were sealed - they are both in their late 70s now! In another case, the husband was just totally inactive but the wife kept her covenants, attended meetings, etc., and eventually and S-L-O-W-L-Y the husband warmed up to things and came back.