The Department of the Children and Youth, Child Adoption Centre in Bangkok can give you all the information you need.
IME - They are very helpful and sympathetic. Well worth a trip to Bangkok and a face to face interview.
If you only need your wife to have sole decision making, the Family Court might make an order of sole custody, but you will almost certainly need the biological father to agree to have your wife as sole custodian. That might need some negotiation and a visit to the Family Court.
If you want to have parental rights for yourself and your wife, that would be more complex and involve official adoption. I guess this would be very difficult if the biological father doesn't agree.
In our case the biological mother and father had abandoned the child, so things were a bit easier. Still, it was a lengthy process but we got there in the end (about 2.5 years). Another year or so to get our daughter a citizenship of my country.
Good luck.
Child Adoption Center
Department of Children and Youth
Ministry of Social Development and Human Security
255 Ratchawithi Road
Ratchathewi District
Bangkok 10400
Tel. / tél. : +66 (2) 3068821; +66 (2) 3068801