I only care for my DSC whilst DP works on the odd ocassion - if he's already agreed to have them and then finds he needs to work. Though the older two (who don't really need childcare as such) come round on a Friday straight from school whether or not DP is there, as it's easier for them logistically.
Depends how you look at contact time really whether it's right or not - is it about your DS spending time with his dad, or is it about sharing parenting - and that includes your ex being allowed to get someone else to look after your DS. Can you just look at it as a good opportunity to have a night off, to work later, or to get out and socialise, or are you feeling that you really don't see enough of your DS? I think overall life is better and more relaxed if both parents can avoid feeling that their time with their children is so precious that they mustn't waste any of it. But maybe that's easier said than done.
It's rather nice that your DS's DSM's mum is happy to get involved - suggests that your DS has been happily accepted into her family, which is good for him.
Doing stuff like baths, reading, etc when he's at his dad's is a difficult one really. Many people would say your ex should be doing these things. But I think it kind of depends what kind of a dad he is, and wants to be. Many men who live with their kids full time leave some things to their partners, and stepping in to fill that role when they're separated doesn't always come so naturally. My DP does most of the care of his DCs but there are a few things that the DSC come to me for rather than him - wanting to be taken shopping, clothes needing fixing, spider removal (!), and a few things that DP was failing at really when on his own (ensuring teeth were brushed) so I tend to do those things. I find they come fairly naturally as I have my own DCs of a simlar age, so I'm kind of doing the mum-things in the house anyway. It seems a bit more odd to me that a SM who doesn't have her own DCs steps into this role, but if her relationship with your ex is secure, and your DS is happy with it, then overall it's probably a good thing.