Your DH’s family are bullies. They went to America for a month, so they aren’t skint are they? If they have 3 DC, and they can’t look after them themselves, they should both look at flexible working, or go p/t. You are not there to facilitate their expensive lifestyle and be their PA for their disorganised bullshit.
You are being bullied, and gaslit. They didn’t get what they wanted, so they are now recruiting other family members to harass you. I’d go ballistic. They have no consideration for your feelings, and they are really disrespectful.
Stick with your guns. But also, you need to anticipate their moves. Can you sit down and work out when they are on holiday, when they are away, and then make sure you work to an opposite timetable. So, if you know they are away, or have a club, or whatever, the first 2 weeks in Aug, make sure you go on holiday the last 2 weeks, go to your mums, etc. Do they have particular days they always need help? Then book your DC’s clubs for that, and then say you aren’t free as you have appointments already booked.
I’d actually not let your BIL’s comments lie. I’d message him myself and say,
“hi BIL, I hear you have been saying how disappointed you are that I cannot look after your DC again next week and how families should help each other out. I’d just like to remind you about the occasions, that I have lost count of, that I have looked after your 3 DC, meaning 6 DC to look after on my own. I cannot even leave the house due to the number. This has not once ever been reciprocated.
Family is very important yes. I’d like to remind you that I too am family, and right now I feel totally disrespected after all the help I’ve given you.
I’m sure you’ll agree that I have done more than my fair share of looking after your children. Moving forward, I think it is best if you find more reliable childcare and not assume that I am will be available, no questions asked”.
If someone in your DH’s family makes a personal comment about you, deal with them directly because most men will not stick up for their wives but try and appease both sides. How do you know your DH isn’t telling his DB, “ I know mate, but what can I do, she’s not budging”.
Deal with BIL and SIL directly. Why didn’t your DH say, this is too much. You need to sort your own childcare.