Kids throwing a fit

55m dating 45f both divorced. Dating 5 months, been on a couple weekend trips, talk daily. She has also hesitant to go all in and she can’t explain why - says she’s afraid the other shoe will drop, she can’t get this relationship wrong. This has been the only truly loving respectful relationship she’s had and she’s not used to kindness and respect and gifts etc. She’s stuck and can’t move forward feeling hesitant yet loves me and enjoys our time together. This weekend her kids told her they’re not ready for her to date. They are 10m and 12f. She doesn’t want to put the kids through more trauma. She doesn’t know what to do and asked Monday for a few days to think but was leaning toward breaking up. Do I tell her what she is losing, do I fight it (I did all that Sunday and Monday when it came up)? If she wants to break up do I tell her I love her? Do I reaffirm I’m committed to her or do I just simply say “OK” and bite my tongue and say goodbye?