What to do; fiance kissed another woman

Yes, this is bad. But is it a deal breaker...maybe not. It depends on how he reacts to you when you confront him. If he owns up to his mistake, and this has never happened before, he might deserve a second chance. But if he denies, denies, denies, then no. Send him packing. Basically, if you think you will spend your life worrying about whether he will cheat again, and you can't trust him, it might be time to end this relationship.