Correct, you can change the vesting on title but to change the loan, it would need refinanced.
Not sure what you mean by "hold your daughters mortgage?" You have a contract for deed with her? You have a regular mortgage on the house in your name? You can add or subtract people for the legal title (ownership) of a home anytime very easily with a Quit Claim Deed. This would not change any mortgage loan. To change a mortgage loan, the loan would have to be refinanced.
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