Thanks for the input everyone!
I ended up calling the Best Western that is right across from the park, and after explaining everything to him, he let me know that it is fine to stay there if you are 18 and accompanying the 17 year old guests. The credit card number did not have to be in any of our names, they just need one in case anything happens.
We are also able to pay in cash, so we'll have no problems with visas or anything.
In contrast, the Desert Inn and Suites required you to be 21 to book and stay. It just depends on which hotel you plan to stay at.