No, you do not want them living that close. I have an amazing relationship with my parents and In-Laws but I would still say no. It's called boundaries and personal space. You'd lose both.

Ask them politely if they could find a place that's still close by but not right next door. They get to be close enough to visit (or even babysit) your son, and hopefully you don't have to be annoyed by them as much.

Don't let them walk all over you OP. Well ... If they buy the house, surprise them by buying your own a couple cities away ... Then again, baby ... Enough said i guess

Offer your house to the loser of the bidding war and move somewhere else.

There's always a bright side OP! Hope everything works out..

I agree with Malia13. Please talk to your parents and inlaws. They might do it for the 'best' reasons but I really doubt this would be a good idea.

Move.

No good can come of this. Explain to them that, should one of them get that house: a) there will be animosity and gloating about it around their grandkid where none should be, b) it will only make the other set of grandparents visit/take your family on trips that much more often, and c) they should think back to when they were in your position, asking themselves whether they'd have wanted their parents living next door. Hopefully logic will prevail.

Move. Move today to an isolated house far, far away.

After they buy the house, move. Far far away.