I don't want my sister-in-law and her new child to travel and stay with my family
Why don't you want your sister-in-law and child to travel with your family?
I don't want to introduce her near my parents because I think my father won't like her.
You should accept your sister-in-law and welcome her with open arms. She is family now; don't oppose her.
I am not a bad man.
No one will think you are bad for considering who to introduce to your parents. Let your parents know ahead of time about her and let them get to know each other over a quiet setting, like dinner. The more familiar they get, the more they might get along.