I agree she would still have insisted on going. If Carlos had been there in addition, though, I expect he'd have stepped up to take over her apprenticeship when Harry pseudo-died.
I don't think there was anything stopping him, except maybe he didn't want to risk the Doom.. Whether he went to C.I. or not, Molly still assisted Harry's suicide, knew that she did, didn't know that he was only mostly dead.. So Carlos could have stepped up, Molly was injured at C.I. so she didn't become the Rag Lady right away, so he could have approached her.