When I was travelling with my daughter when she was small enough to need to use a lap belt, the cabin crew usually encouraged me to use the seat next to me for her if it was empty, and if it wasn't either found me a pair together or offered the passenger in the middle seat a move if possible (an offer which was usually accepted with alacrity on their part!). All of this was offered by the crew without me asking for any preferential treatment by the way! I don't think I ever had to have her on my knee for the entire duration of the flight - just take off and landing and the occasional cuddle when needed.

In this situation - as neither passenger had paid for exclusive use of the seat, both had an equal entitlement to use the space, but IMHO it was churlish of the aisle passenger to actively discourage the mother from using the seat - after all - its impossible for someone with a child on their lap to use their tray table or get to the overhead or even under the seat in front of them if supplies were needed.

Most reasonable people would have had some consideration for the comfort of both the mother and the child - after all the child wouldn't have been invading the aisle passengers paid for space or fighting for the armrest like say a passenger of size - or even any other adult would.