I currently own a manufactured home in Michigan. It is located in a park that I rent the lot from. Due to the economy in MI, I had to take a teaching job in NV. I have been paying double payments for the last 10 months. My park does not allow renting. Before I left, I asked if I could have someone move in (a friend or family member) to take care of the house while I was gone. I was told they would need to fill out an application to be placed on the lease.

Now, my cousin, who is 19 and employed full time is able to move in and help me out. I had him go to the park office and get an application like I was told. He was told that they most likely won't approve it because the lot is occupied. I called the park back and explained what I was told before. They told me they do not allow renting. I said, I am not renting, I need help taking care of my house when I am working. They said if I'm not living there, I am renting it. I said I only live there on breaks from my job when I visit MI.

I have rented from this park for over 9 years and never been late. Do they have a right to tell me I cannot allow a family member to live in my house while I remain financially responsible for everything?

I am completely frustrated and would consider just abandoning my house like hundreds of other peopl in the park already have. I cannot sell the place because, again, there are HUNDREDS for sale in our park.

Any suggestions?

Yes, if they have a rule that the person on the lease must have their residence there and they are not allowed to "rent" it out to anyone else.
* which is what you are really doing but in this case it is a family member.