The thing that strikes me here is that having a terminal illness does not suddenly turn a person into a lovely version of themselves. If they were an arse before, they still will be. If they were a kind considerate person before, they still will be (albeit not always because they'll be in pain, struggling with processing their situation etc).
I would say you need to find a way of feeling you are treating your in-laws with decency so you can live with yourself, but don't buy into the "poor sick MIL thing" that means you're not allowed to challenge or have control of your own life. You are allowed to not like her, or not like the position you feel manoeuvred into. But you need to decide what you're going to do instead, for your own mental health. As they say "whatever you aren't changing, you are choosing" so if you do nothing, you're choosing to let this happen. You may feel you haven't the energy for it, but I suspect once you start the release of standing up for yourself might be quite energising!
Even if the in-laws were amazing people in full health, I wouldn't want to rely on them for all the childcare while I worked. It's not fair on them (tiring, relentless commitment, means they can't be spontaneous to do their own thing for a large part of the week, pressure and worry about letting you down if they're unwell, plus risk they will catch lots of things if looking after your unwell child). It sucks the joy out of a family relationship and makes it transactional.
Stick to paid childcare for three days while you work. Talk to your husband about a regular time for your in-laws to still see your child, once you've figured out something that won't fill you with suppressed resentment. Something like all having tea together on Thursdays or something, so it's a thing you would be doing anyway and isn't extra effort and doesn't interrupt every weekend so you can choose extra activities to invite them to without it being set in stone