Thank goodness this never happened to me cause my parents were good parents, it’s just as much the childrens home as the parents and children should be allowed to say “I don’t feel comfortable with another man or woman living hear” Its the parents responsibility to make sure their children are comfortable and feel safe around a new adult. The parent should plan a public meet and greet parent, child, step and after each one the children should have the right to say no more and it end there.
I don’t think kids should get a veto but do think kids should get to voice their input and you should listen to it and address it. When I got together with my now husband, 2 years dating then we moved in together, 2 years living together before we got married. Our kids all like each other and are glad to have more family. When we first moved in together, the teenagers played beer pong and bonded, lol. The little ones were happy because they got an upstairs. It was obvious everything was working out.
No I didn’t ask the kids’ permission, but we are close and they are open with me, I trust them to tell me how they feel and oh boy they do.