Hello and Thank You for using Just Answer. It would not be a wise idea to allow this man to spend the night over your house with your children there or not there unless you were soon to be married.
You can leave your 14 and 16 year olds at home for a few hours while you go out on a date with this man. There is nothing wrong with that. Just be open and honest and tell them exactly where you are going and what you are doing in case they need to contact you. Hopefully, they are responsible teenagers to be left alone at home for a few hours.
As for spending the night at his house, this is a really delicate situation. Of course this places everyone in a very awkward situation. Your children's minds will wander as to what exactly is happening while you are at his house. If at all possible, have your children spend the night over a relatives house while you spend the night at your man's house. Tell your children that you are going to spend some time with your male friend and will return the next day. They already know that you are spending the night with him so you cannot erase that fact. They are old enough to accept the fact that you have a boyfriend. You have been divorced a while as well. It sounds like you may be a little ashamed. Ask your children how they feel about the situation as well. Keep their feelings in the forefront too. This will make everyone happier in the end because I know that you want everyone to get along.
Hope this helps.