Ok. So your father is concerned about the family reputation and what "log" will say, yes?
That does create some problems.
You need to take this in a step by step manner.
The first step is the most important. You have to make a choice. Are you going to stay with your husband or not? If it's "stay," then you should consider trying what others have suggested...being more firm in future, getting a separate household for yourself and hubby, etc.
If it's "leave," then here is what I would suggest. Don't talk to your dad right away. Speak to another trusted family member. Preferably someone your father respects as well and someone who has observed these greedy tendencies of your husband's and his family and who rightfully agrees with you that this is highly unfair and uncool. Discuss this all with this family member and ask her to be present when you go to your father. Both of you speak to him. And explain (in addition to all the hardships you AND your father have had to face by giving in to these unfair demands) that though he may save face now, how will he feel if a most beloved daughter is abused and used throughout her married life? Ask him if the pain you will doubtless go through is less important than the family izzat. And if he says that things will settle down and/or you will "change" your husband, ask him honestly to tell you how well that's worked out for other women whose families told them the same thing. Your dad has been around a LOT longer than you and he has doubtless heard worse stories than yours regarding girls marrying into greedy/insensitive/cruel families. If he is honest, then these remembered stories will make him pause before he does something so extreme as to refuse you outright or to Allah forbid, kick you out.
You know your father best. If you feel that this may work, I say you go for it. If it doesn't work, please keep us informed as I'm sure there are other alternatives out there that members can suggest.
Also, do you have a job of your own? If so, then I'd suggest you start putting your paycheck aside and depositing it in a bank account that belongs ONLY to you. I'm not trying to scare you. I'm just trying to suggest the practicalities that every woman regardless of her situation (good or bad) should consider and take care of.