I think the problem here is that we don't know why the mother is asking OP to take the DC.
If it's just because it's "his time" then I agree, it's a bit shitty.
But if she has other responsibilities, like work, that she can't rearrange then I don't really see the issue.
I also don't understand step-parents - of either sex - who don't seem to have much of a relationship with the children, especially when they have them in their home 50% of the week, as is the case here.
Having been both the step-parent and the step-child, I just don't get the mentality of "not my kids, not my problem" that some step-parents have. While I agree the responsibility lays primarily with the actual parents, I think step-parents do have a supplementary role to play as they're part of the family unit. More akin to a much-loved uncle or aunt, not the primary care-giver but someone who could and would willingly help out and has a good relationship with the child.
I can imagine with her DH in hospital, it would be much easier for the OP to have as few DC as possible to look after and organise, so I completely understand why she'd want the mum to have them. But what I don't understand is the whole attitude of "they're nothing to do with me" which seems to emanate from her posts.
I know many on MN will disagree but I think when you create a blended family then you acquire extra responsibilities. That applies to either sex. You don't become an extra parent, but you do need to pull together as a family unit and that might mean sometimes needing to step up. Male or female. No difference.
But in this case, I also suspect there's a whole back story here that we're not getting.