I think that depends on what is meant by “bad relationship.” If the person aspiring to religious life sins against their parents by gossiping about them, treating them cruelly or with aggression, or willingly harbors ugly thoughts about them, I would like that person to confess and repent of those sins before entering religious life.
However, if “bad relationship” means “we don’t agree on things or don’t particularly enjoy each other’s company, but we’re cordial,” that’s a horse of a different color. You must love them, but you don’t have to like them.
I would advise someone in both situations to try to mend fences. Even if it doesn’t work, you tried. You give up so much to enter religious life, it’s good to give up any resentments and old hurts as well. You get to start a new life with a lighter load.
May the dear Lord bless and keep you!