NY residential landlord tenant law, dangerous conditions, lead paint, landlord's duties

Lead paint issue with child in NYC apartment: I live in Brooklyn, NY. Recently, my 13 mos. son tested for a 7 lead count in his body. In response we asked the landlord to seal up all cracks in apartment; and they actually brought in an expert to check the lead content of the apartment. The expert recommended replacement of doorframes, doors, windowframes and shutters. Then I received a call from management company on behalf of landlord telling me that 1) because the landlord cannot afford the entire renovation and 2) because they do not want to take on the liability of my son being possibly tested as a #10 (for then they have to do full renovations) and finally because 3) They did not sign the lease for the next year, we need to vacate the apartment.

What our our rights here? Please help us...and also note that I have been renegotiating lease since August 23rd, and have extensive paper trail of written and accepted offers from the landlord on email.

Hoping at the least, if we need to move, that our expenses will be paid to do so. (Moving costs, broker's fee, etc.) - Is this your question? Add additional information