I know as a single father, that it is a very tricky subject. If you are given the chance to meet the children, than it must have been serious. I date and have only had my kids meet two of prospective girlfriends in the past few years. SO you must have been something special, from my point of view. I would say be yourself, kids seem to be a better judge of character than adults, its only as we become older and more trained by society that we lose that sixth sense. So if your nice and you like them and they like you your in.. Good luck