Aside from SN or disabilities, it doesn't take two people to look after a baby on a flight.
You just take the baby back and forth between you when the seatbelt signs are off to ease the tedium.
Whoever doesn't have the baby can then have a proper rest, rather than having two half-rested parents. Bliss!
The mother was definitely being unreasonable.
I could understand wanting to be near small mobile children in the case of evacuation. But this was a baby so on their knees anyway. Can people not manage a whole 10-hour flight sitting next to a stranger?