Your H does the same thing my H does - puts the cart before the horse and turns the blame around. *HE* could have supported his children voluntarily... Why should it be on you to give him an ultimatum, threatening legal action? Is he saying he has to be threatened to do the right thing? Sounds like he's venting his anger over being forced to do something he didn't want to do, and making it your fault that he financially deserted his family.
Now, on your side - if you want him to take the kids when you're sick, you're going to have to encourage him having them when you're well... You may enjoy your time alone more than you think.
When it comes to work - so far, I got a part-time job that gives me a small, but steady income. I also have a couple of other part-time income sources, but they are less predictable. Unfortunately, I have health issues that will make it harder for me to handle full-time employment, at least for now.
M 16 yrs, WH62, P54 3 adult blended kids EA 11/13, BD1 6/14 PA fall 14, BD2 2/15 Piecing 2015, BD3 12/15 Separated 4/16 WH moved OW in 5/16 Divorced 6/15/17