My question involves a child custody case from the State of: New York
I have a 21 month old son who has lived with me since birth. I filed petitions for both custody and support back in March 2011 in NYC. His father has had very little involvement in his life. We lived 1 block away from him while in NYC and he rarely came to visit/did anything for my son. His paternal grandmother was the one with more involvement. So in June 2011, I had no other choice but to move out of NYC because of babysitter issues and frankly not enough money to live for me and the baby. I have proof of my monetary problems and also proof where I had to break my lease and am STILL paying back rent that I owe from earlier this year. I moved to Kentucky to live with my parents. I informed his father of this move in Dec '10/Jan '11.
We get to court last Thursday and his father contested my petition and now wants joint custody. Alledging that i'm "unfit because of the decisions I make" (say what??) and have prevented him from seeing his son. Since we have been gone (my son left NYC in April with my parents), we have not received one phone call, email or text from his father. None of my contact info has changed. The only thing we have received is 3 child support payments that just began this month (due to garnishment of wages). We both now have court appointed lawyers and have a hearing in September to discuss visitation.
I will not do joint custody and I refuse to foot the bill all the time and do all the traveling. KY to NY is about 740 miles one way. I am starting 2 new jobs August 1 and can NOT afford frequent trips or much time off as both jobs are PT and only one offers benefits after the 90 day period. I am proposing 1x weekly skype visits, frequent phone calls and 6 yearly visits - 3 weekends (1 weekend about every 2 months) in which we travel to NYC, 1 week and 2 other times during the year in which his father must come here (anytime from 3 days- 1 week for bday, Thanksgiving & Christmas), to be modified as needed the older my son gets. Is this unreasonable? and what are the chances the court would agree to that type of arrangement?
Thank you in advance!

