can i claim rent on a vacation home that i rent in a different state

Do you mean you are the owner of the vacation home and rent it out to other people?    Or do you mean that you rent it for yourself when you go on vacation?

I pay the rent.  I let my daughter live there but the lease is in my name and stay there when I go on vacation 

There is not a rent deduction or credit on your Federal return.  If your state has anything for renters you will be prompted to enter your rent info when you complete your state return.  As far as I know, the states that have anything for rent are Arizona, California, Connecticut, Hawaii, Indiana, Iowa, Maine, Maryland, Massachusetts, Michigan, Minnesota, Missouri, New Jersey, New York, Rhode Island, Vermont, Washington DC, and Wisconsin.