Enjoy your new relationship and leave your sons to come to terms with it in their own time.
Don't invite them when you expect your friend to be at your place. I'm assuming you are not living together? If they do turn up when you are with him either in your home or outside it, just say casually, "As you see NN's here, it's been ages since you saw each other, hasn't it?" thus signalling that you expect polite, adult behaviour.
If they are rude or offhand, tell them that their behaviour disappoints you, either at once, depending on what is said and how, or afterwards. If you like, point out to them that you don't love their father any less for having started a new relationship after his death. Presumably, he would not have wanted you to be miserable for the rest of his life.