Your children are 50% of both of you. That was also 30 years of marriage which is a long time for a marriage. It is probably confusing on how they are supposed to feel, especially if there is someone new in your life.
I would focus first on yourself and take care of yourself. Your kids are adults. I would not push your new relationship on them too much This is your life. Take time to just enjoy your life and make sure that this new relationship is the right relationship for you. If anything, this new person is only going to be a friend to your kids anyway. But hopefully, if this relationship is more long-term they can see your happiness and learn to love her as well.
Before I met my husband, I dated an older guy whose wife had recently passed away who also had teenagers. I am really glad I did not push anything with his kids and was just their friend. In the end, that relationship did not work out.
It is going to take some time to let things heal. I can only imagine that it is different for you to be dating someone else as well as wondering if this new relationship will work out and if they should get close with this new person.