As for the insurance issue - you can COBRA your coverage for three years after a divorce, and thanks to Obamacare, you can buy insurance after that without concerns about pre-existing conditions (Thanks you Obama! He saved my butt).
I think your ex should have to pay your COBRA payment since he is divorcing you in the middle of a severe medical crisis. Also spousal support should reflect the fact that you will be disabled during your chemo treatment (seriously, who is going to hire you while you are puking your way through chemotherapy???). Your ex is stupid for pushing the divorce right now, he'd be better off once you are through treatment and able to work, but then, we already know he's an idiot.
As for the idea of divorce itself - you need to let it go. Trying to hang on and fight the (possibly) inevitable is only going to make YOU sicker. Let go or be dragged. Plus, if you divorce NOW, you can preserve your share of marital assets for your kids in your will. If you happened to get hit by a truck before the divorce is final, all those assets go to your H, and who knows how he'll waste them on OW.
And ignore all the ridiculous nonsense. No, he didn't stay with you for 20 years and make 4 kids because he was miserable in the marriage - they always rewrite history. And YOU know the benefits your kids got from homeschooling, the in-laws opinion doesn't matter a bit. (Btw, do the in-laws even know about your recent stage 4 cancer diagnosis? If they do, they are despicable people - but then again, it's likely your H hasn't told them.)
He doesn't want full custody, he's just trying to use the threat to get you to go through with the divorce. Throw him off guard - let him know you're more than happy to divorce him ASAP if he agrees to your terms.
I'm pretty sure if you end up in court, the judge is gonna look kindly on a homemaker with stage 4 cancer.
As for visitation - it's rotten that your ex is being so insensitive. Nonetheless - you need to figure out a way to facilitate his relationship with the kids. One reason is so that he can't pull that "parental alienation" crap on you (as if his affair isn't reason enough for the kids to be alienated from him!). The other reason is because, if you don't so well (although I believe you will) he IS their other parent and it will be easier on them if they have maintained some kind of relationship with him.
As for keeping them from the OW - that's a losing battle in the long run. You might get an order for now but once the divorce goes through, they'll still be exposed to her. So pick your battles. In fact, if they have to be around her and are nasty to her as a result, it might scotch the relationship between H and OW altogether! lol (Watch the movie She DEvil with Roseanne Barr if you want to have a good laugh about this).
Don't fight the divorce, just fight for the best financial deal for you and your kids. If he's so hot to get divorced, you may have your best shot at a good agreement now.
