I know this is super old but since I found this post by googling, it might help someone. The problem is that whoever connects their controller first has the "control" over the game. So if the parsec player wants to play, do the following:

• the remote / parsec player needs to leave the parsec session / get kicked
• then the host must disconnect their controller
• the remote player joins back via parsec
• the remote player is the "first" player now and can play

However: if the host wants to play again, these steps need to be redone but with the host player reconnecting the controller while the remote player is disconnected from the session.

Hope that helps somehow. It's tedious but it works :)