I'm trying to transfer my Probation to another state and its taking forever. I have a child at home and that counts as my blood family, however I'm not married to my fiancé.

Does common law marriage apply to a probation Transfer?

https://www.askmehelpdesk.com/criminal-law/how-transfer-probation-115783.html

1. you are either married or you are not.

2. in the US very few states reconise common law marriage any longer ( and have not for years)
And those that do, often require specific needs that are required

So how long is "long" 1 month , 3 month,

What have you done to apply, have you sent in a written request ?
What has your PO said about it.