…well, when one of my neighbors and I disagreed on how a particular fence should look, he ended up constructing a fence on his side of the property line, at his cost and left the shared fence intact.

I think in your particular case, if the only thing you’re worried about is your dogs, that would probably solve that particular issue.

But if it’s just a repair thing, might as be better off just finding a handyman and doing the repairs, and then sending the repair bill to the property management company (1/2 of it anyway)