My married daughter has a large credit card balance due to which she is paying a 16% monthly charge. May the father lend her the money to pay off this loan where she will pay me monthly and she would pay me 4% monthly instead of paying the credit card company ? Please tell me what you base your answer on, and how can this be done halachically?

You are not allowed to charge your daughter interest even if this is less than the bank rate. You are allowed to lend/invest in your daughter through a "heter isska" (the principle behind this is that part of the money you give her is an investment which she returns with your share of the profits; if she can prove - you can require very stringent proof that makes this extremely difficult - that she made no profit from the time you gave her the money she does not return even that part of the money which was an investment. If she cannot prove that, she can pay you a flat rate of 4% instead of calculating the profits coming to you). The exact wording of a heter isska can be found in the Code of Jewish Law by R' Shlomo Ganzfried.