Baby mama drama i need your opinion!!?

soo before me && my boyfriend got together he had a baby with his ex.. but him && his family are all doubtin that its his baby.. he got out of jail April 4th so I'm using that as the earliest date the baby could be conceived.. cuz he was locked up before that so there is no way he could get her pregnant before that date.. the baby was suppose to be induced December 16th but she had her a day early.. doctors usually induce labor if the baby is past due correct?! do yall think these dates add up?! the baby has blue eyes && both him && her have brown eyes well my boyfriends eyes are hazel but basically look more brown.. another reason that everyone is questioning if the baby is his.. is because she cannot stand me at all && has been puttin me through hell with stupid drama && if she really hated my boyfriend && me like she says don't you think she would put him on child support... i know a phaternity test needs to be done.. but she told us that the state will do it.. she is on food stamps && they need to verify both incomes.. ++ those tests are hella expensive im considering takin her on Maury haha jK!! but at least he would do the test free let me know what yall think!! thanx!