Answer
Wa `alaykum as-Salamu wa rahmatullahi wa barakatuh.
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
There is no riba in what you described except the student loan.
Responding to your question, Prof. Dr. Monzer Kahf, Professor of Islamic Finance and Economics at Qatar Faculty of Islamic Studies, states:
You need to understand what riba is and what the credit card system is. Riba is any increase in a debt or loan through time that is because of a time period between taking a loan and paying it. I do not see any riba in what you described except the student loan which I will come to discuss.
1- Credit cards: this is a card issued by a bank. When you use it, the bank pays on your behalf to the seller. The seller gets its money as a price of the sale and this has no riba. When your father accepts credit card payment, all that means is: the bank pays your father instead of the passenger, it is the exact amount with no riba involved at all.
2- Now for the passenger and similarly your sister who has two credit cards, the issue is a little different. At the end of each month, the bank sends a bill to her for all the amounts she asked it to pay on her behalf. If she pays the bank with a certain time called “grace period’, she will not be charged any riba. This means that as long as your sister pays the bank’s bill every month on time, she does not have to pay any riba.
If the passenger (or your sister for similar reason) delays payment of the bill beyond the grace period, then they have to pay interest to the bank; that is riba and too bad.
Cases 1 and 2 above mean that whatever you receive from your father and sister has no riba at all. It is the pure earning of their hard work as a driver and as a hospital worker. It does not matter whether your father sends you money from cash payments of or from credit card payments of his passengers. Both are halal and have no interest elements at all. The same holds true for what you get from the salary of your sister as long as she does her job with honesty.
5- The student loan that your sister has is certainly interest-based. May Allah forgive her. She did a mistake by taking it. But wait a minute. She may have good reason for that, Allah knows and we do not judge people. Do not pass a judgment on her. She should try to pay it as soon as she can.
6- Just be thankful to Allah that He gave you such good father who cares (because he sent you money from the cash not from the credit card earning as he was under the impression of doubt about it. In fact, there no doubt at all about that because he only receives the price of the ride, no difference between cash and credit card payments. And be thankful to Allah that He gave you a good sister who cares and sends you money from her work. And be also thankful to them both father and sister.
Almighty Allah knows best.