I am sorry - we are all working lawyers and I have been in court all day
I am not sure what the deadline is as your partner certainly cannot simply refuse to return the child after contact I am afraid
With regard to the property your partner can give his ex "reasonable written notice to leave" - at least three months notice - and at the end of that time he can change the locks.
The risk is that his ex will apply for an Order under Schedule 1 of the children act allowing her to remain there for the next 15 years - or until she cohabits - however that would give him the chance to argue that she should pay some form of rent whilst she is there
With regard to the child there are a number of options open to your partner
If he is certain that the child is at risk in the care of his partner he can make an urgent applictaion to the court using a form C100 for an order that the child lives with him until there has been a proper assessment of the current living arrangements.
Alternatively he can ask for a Prohibited steps order preventing his ex from allowing the child to meet or spend time with this new partner.
It would be unwise to issue in respect of both the property and the child at the same time as his ex will try and argue that he is making up his concerns about the child to get her out of the house
I hope that this is of assistance - please ask if you need further details