Does a man's concealing from a girl's family his previous marriage and the fact that he is a father of two children invalidate the engagement Islamically, if the girl herself has known and consented?

Not informing the girl's family about your previous marriage or that you have children is not considered deception, as you are not religiously obligated to inform them unless asked. If you are asked, then you must inform them, because concealing it would be deception. If they approve of your marriage after learning about it, then all is well; otherwise, look for someone else while performing istikhara.