Imo it's fair of GF to ask you communicate about your son's illness, especially if he's going to come around near her and the baby later that week. However, if she's really just using that as a way to keep him away and drive a wedge between you that is a serious issue you can't accept and need to have firm boundaries on. I've said this before...while her and your baby are priorities your other children have to be priorities as well. She has to accept you have other children and her baby isn't the ONLY priority on your list, or it'll never work between you.
As for the cleaning...do your fair share but don't be a martyr and allow her to manipulate you into doing everything.
I agree w/others the way this is going you need to consult a L ASAP to understand your rights and how child support plays out with multiple kids with two Exs.
Me:39 Ex-W:37 M:7 T: 9 S:6 D:3 BD/IHS/Confirm EA/PA: Feb '20 OM1 affair ends: May '20 W/OM2 & moves out: June-July '20 W files for D: Jul20 OM2 confirmed: 9/2020 Divorced: May '21