Yes, lots of emotional brinkmanship in this one. Grandparents can absolutely be toxic enough to warrant no- or low-contact, but I don’t see where OP has indicated they’re close to that point. This is a retrograde joke from the grandpas, but in the US it’s also utterly cliche and doesn’t necessarily imply much. Something along the lines of your suggestion could absolutely be a better option in the early going. You could even make it more casual at first: “Nah, this one’s going to be able to take care of herself. We’re making sure of it.”