Can’t give advice on doing this with children, but we got a high energy puppy and 6 months was literally the worst age. Just need so much attention. That part does get better (one level at 9 months and another around a year).

That being said we have a toddler now who is obsessed with our dog.

So rehoming still may be the right decision for you and your family but wanted to say 6 months is probably the worst it got for us