No - I was told by the head guy in immigration at POP airport that, so long as you and the baby entered the DR alone and leave alone, you do not need a letter from the father. This was also confirmed by staff at the immigration office on POP.
If however you all entered together and you and the baby were to leave without the father, then yes, you would need a letter. In fact it's more than a letter that you need.....you need to visit the immigration office in POP to get a list of all documents required. These include a notarised letter of consent from the father, a copy of the picture page of both your and the baby's passports, a recent picture of the baby, ....and....I can't remember if there is anything else. Once you have all these documents you then need to go back to the immigration office in POP where they verify them and get you to fill in another form stating flight details. It's a bit of a procedure so you should leave enough time to get everything done.
Daydream