@MsHardy you wonder 'what happens going forward'. Although you've had some really helpful advice on this thread, there is some caution needed in how you proceed.
Controlling people (if he is genuinely controlling rather than just a selfish, lazy, entitled a-hole) will look for any excuse to isolate their partner from sources of strength and support. So there's a risk that if you go in with a 'f off out of here BIL' approach, he will persude your dsis that you are somehow not nice, mean or disrespecful, or don't love their dc enough to help them sleep, or whatever... He will try to stop her from contacting you because you are a 'bad influence'. I imagine that however hard this is, your sister might go along with it 'for an easy life'. Maybe only contacting you in secret.
Your sister has been capitulating to his demands for a long time. If you tell her that she and dc are welcome, but not her husband, how do you think she coud possibly say that to him? She might find it easier to give in to his demands than yours, and again you risk reducing or losing contact.
If you genuinely think he is controlling, and therefore abusive, it is worth taking professional advice about how best you can interact with your sister around this, and support her.
On the other hand, it is possible that BIL's life and upbringing has been such that he expects every woman to jump to his demands, with no need to be grateful, or to consider the impact. If he had a mother, who did everything for him, never pulled him up on his entitlement, he needs to be re-educated. It doesn't really sound like your sister is up for this. But if he's like this (rather than controlling), he might just say 'your dsis is a mardy cow, you go and visit her, if you like, but I can't be arsed'.
Sometimes the outcome is the same - your people pleaser dsis might feel that leaving him at home while she visits you is somehow 'not being a good wife' (and appearing to the outside world like a good wife and a happy family, may also be really important to her). She may either try to persuade you to change your mind, or she might stay at home with him, so the poor darling isn't upset.
It is such a terrible dynamic.