I think it would be better in any circumstances to fight it while here in the UK, you are an established family unit and I presume managed to live together without resorting to public funds. To send you back to the PI they would have to provide travel documents for the baby so you could delay that process.
Be careful in your choice of legal representation, I am sure if you stick to suggestions above it would be safer, and, if possible, make an appointment to meet your MP rather then write to him.I think you have a good chance of resolving the situation.
