Even if they signed lease, they still can move out with one month notice because of the uninhabitable condition. It will be ok to follow 老貓 advice.
By the way, you always can find ways to force the landloard to move fast. Especially the tenant is pregnant and they have a young baby. It is a wisdom how to do it. Write to the landlord and agent that both the pregnant wife and you kid get sick because of rotten carpet. Have both landlord and agent to sign that they have recieved your complain. I believe they would move much faster.
