If we go with the "Karin is the mom" theory, the moment she got preggo the child should have become top priority for her. That means owning to the fact she has the duty to care and nurture for her child for the rest of her life. She has 0 excuses, the only thing she needed to do was to tell Sasucakes and I bet he would have gotten her well established and protected in Konoha under Naruto´s protection (or are we going to pretend Naruto would let Sasuke´s child abandoned just because Karin is the mom? Me thinks not)
If an adult think he/she is unsuitable to become a parent with their current SO for x, y or z reason, then it becomes his/her responsability to prevent this (an unwanted pregnancy) to happen. Saying "opps!! I´m not parent material/ oops!! I can´t take care of a baby right now/etc, sorry baby!!" is the most despicable and irresponsible attitude ever.
If Karin is the biological mom and there isn´t surrogacy involved, then I´m sorry but she´s been damaged as a character with the deadbeat parent card. Why? because she´s perfectly healthy, the child could have been raised by her in a safe environment (if Sakura could do it I don´t see why Karin couldn´t), and she still put working for Orochi as something more relevant than being mom.