Extending a contract

If they are not paying for your assignment housing in your absence, then yes, they should pay your round trip home. It is a legitimate expense.

You are worth roughly $5,000 gross profit to your agency for a three month assignment. If you do not renew, they may lose all of that as some other agency may fill your spot. You also have proven success at that facility, something both the facility and the agency do not know about any other candidate. So you have some pull, but only if you are ultimately ready to walk away from the renewal. Ideally, you shopped around before accepting this assignment and know you are being paid well. If you are, asking for a couple more dollars an hour would be reasonable and not very confrontational. If you don't know if they are paying you a competitive wage, you need to start calling other agencies now! If you find out your pay is not competitive, you should try to negotiate even harder to bring it up to market price - and commit to walking away when they refuse. In this case, you are better off working for an agency that values you as a profit center and pays and treats you accordingly.

By the way, another path may occur to you, switching agencies for this extension. Usually not possible because of the contractual terms the agency and their vendor agencies have with them (often reflected in your own contract). In fact, not worth trying. Wait for the non compete period to end before returning to this facility and work instead for one of the agencies you found that pays competitively.