@TatianaBis
If the older kids were own you'd have to get up to do the school run, new baby notwithstanding - presumably you'd share it with DH.
Once you're married to someone with kids - they are your kids.
The place to cut back is on ex-wife's days - that's definitely not necessary.
@FeckingPuddleDuck
I don't get this argument. It always comes up on step parenting threads. You could say it about anything. If X was Y you'd have to do Z. Yeah but X isn't Y so it's irrelevant.
If the Dad is sharing the school runs with anyone it should be with his child's other parent, their Mum. That means him doing it his days and her doing it on hers. That is the children's parents sharing the school runs.
Most people don't have a third person they can dish out or 'share' their responsibilities with and surprisingly most people manage to get their own children to school between two able bodied parents.
All of this. Totally agree with feckingpuddleduck. Why on EARTH is this school-run, the OP's responsibility? As you say, most other couples manage to get their OWN children to school between the two able bodied parents. I think the DH and the ex are taking the OP for a mug tbh.
Yeah I bet the ex was grateful when the OP offered to take her kids off her hands for the school-run.
The school-run is stressful and horrible for many, and the ex was probably rubbing her hands with glee when the OP offered to take it off her hands.
And now the OP is struggling, all the ex (and the OP's DH wants,) is for her to go back to resuming duties as before, and ASAP, because it's inconveniencing them! No thought for the OP, or how tired and frazzled she must be, just 'when you gonna resume the school run for our children?!' Fuck that! They need to sort this out between them, this is NOT the OP's responsibility.
Why the hell should the OP be dragging herself and her new baby out of the house at 8.30am, on potentially 2 hours sleep, for someone else's children? And NO when you marry someone else, their kids DON'T automatically become YOURS tatiana! . 
Oh and YANBU @TangledTangles