My thought was there can't be a father around because marky appears to still be living at her mother's and it wouldn't make sense to keep the father's identity a secret while posting her daughter's face everywhere.

BUT if the father happened to be a semi-famous comedian / internet persona with other baby mommas out there these facts suddenly don't seem so strange. He would want to keep it a secret and I bet he would offer financial assistance to her and her mom while she stayed at home and cared for the baby. The boy on her insta could be another one of his children that she during the day.