It’s so hard isn’t it OP. I’m a lone parent with a 2 yo who has rotten luck health wise, including hospital admittance. It causes me endless anxiety and I came close to losing my job soon after getting it.
Things I’ve done to mitigate the damage:
If DS is sick I make sure I’m available on email or phone for questions as much as possible
I never ever slip a deadline. If I’m looking after DS all day and there’s a deadline- I work all night to meet it. Caffeine is a lifesaver.
I show that I’m trying to cover with childminders etc- even if they can’t do it last minute, I keep a paper trail.
I work fucking hard, all the time. I make myself indispensable to my boss.
I apologise- even when I think “I can’t help this”- profusely.
This is all shit; I hate that I live in constant fear of coughs and colds- DS is asthmatic so these can mean a week of work at times. But my boss now knows that I am 100% dedicated to my job, and if they bear with me - let me work flexibly when need be - they’ll be paid back 100fold in my loyalty and dedication.
They also know they’re paying me significantly less than someone with comparable experience would get in a corporate organisation (I’m third sector)- and they’re unlikely to find anyone with my skill set and experience within the sector, however much money they paid.
I can only suggest that you go to HR not defensively, but ready with a plan of how you will put measures in place to support you when your kids are sick.
Good luck.