What a mess, I feel for you.
Children are terrified of being rejected by a significant adult figure. They don't see what adults see, they assume they know by what they experience, as it all a child has to go on.
They may make rash assumptions, possibly fuelled by their mother.
What I read from this is two children wanting to have time with their dad. This is being reduced or not of the same quality time for the little time they get.
I'm not saying your feelings are not natural, they are. I'm saying look at how the other children in this relationship are seeing it.
If they were with you both full time, they are likely to still take no interest in a baby, this is normal.
All they see is another child in the mix that's taking away from what little they get.
I'm from a big family. My mother always said, the new baby won't suffer, it's the older children that have to be centre of attention. Their worth and their valued position in the family should be celebrated at this time.
It's easy to forget how lost they can feel when a new baby is showered with affection.
This is tenfold when the children are not living with you.
Your baby will thrive, for your other children to thrive too you have to put them centre stage.
Blended families are so hard to get right. But done right they are amazing. Good luck and best wishes.