This may not fit with the OP's plans due to timings, but my son will turn 2 while overseas and we were able to do the following with a 2 flight return (one each-way):

Outbound flight is when he's under 2 - classed as an infant, must sit on adult's lap

Inbound flight is when he's 2 - classed as a child and has own seat

We paid the infant fee for the whole booking, but had to pay £15 for booking by telephone as they said the booking couldn't be made online but were unwilling to waive the fee (I didn't push it as we were getting one leg of the journey practically free). We need to fly at the times we are flying so were not intentionally trying to exploit this, but we knew other people who'd done the same on VS and I called BA before booking to ask how it would be handled.

If you can take the full outbound flight when your child's under 2 then you should be able to get the whole ticket at infant fare and a seat coming back.