This is not about a playpen but you being respected as the mum. You need to talk this out with dh. What right does he have to allow fil to over rule a decision you and dh made as a parents. If dh changed his mind he needs to talk that through with you.
While normally it a equal decision over whether you buy something. When it a tool you need to get through the day safely than and you are the one who is doing all day everyday than you say is more important.
Seriously get this sort red while bub is little or your life will become a living hell. You are the Parent Therefore You Need To Make The Decision Not Your pils.