Re: We both firm to marry but not both families
You obviously need to find someone that the professor will listen to.
4:19. O ye who believe! Ye are forbidden to inherit women against their will.
There is a hadith of the Prophet (PBUH) saying that: `the virgin is to be consulted in her marriage.' Hence to marry a person against her will, i.e. forcing her, is a negation of that right.
This means that whomever her father wants to marry her off to will be commiting a sin by marrying her against her will.
Islamically, no one can force a girl into marriage so maybe you can enlist the help of a local religious leader to talk to the professor and explain that he cannot and should not marry his daughter against her will. If you know the mosque that the professor goes to (I am assuming that he at least goes to Jummah even if he is not a regular prayer) then talk to that Imam or religious leader. The only danger of this is that professor sahib might get angry about his private family business being made public so ask your fiancee who to go to.
Also, it would be helpful to know how many members of the girls side support her marrying you. If she has the majority of the family supporting you, you guys can try to get their support in convincing the father. If the whole family is supportive except the dad, you can go ahead anyway. If there is an elder like professors father or another elder that he looks upto, try to get him/her on your side.
There is one more step but this is very extreme. You can do a nikaah with all supportive family members present but not the rukhsati to use that as leverage. However, there is discussion as to whether a girl can marry without her fathers consent. If you are going to consider this option, please consult a local imam to confirm his viewpoint and also ask for references backing his opinions. I have heard imams give opinions and then when asked where it was written actually say...bazoorkon sey soona hai..as if that is authentication.
Please keep us posted and good luck..you are in a very difficult situation!
Oh..and one more thing..has your family agreed to change the issue about your sisters getting married first...or was that still a condition even though they went to meet with the professor?