You'll absolutely need a bathroom, which most 13'ers don't have. Those that do give up a lot of space and lack a dedicated sitting/eating area, so you'll have to make up the bed and take it down daily. You may also find a 16'er easier to find and cheaper, because there are a lot more out there with bathrooms. That said, if you still decide to go with a 13' bath model, Floyd is the resident expert at making that layout work for long-term use. He's done some nice mods, particularly with the dinette area, making it more flexible for day/night use.
Couple of concerns about living in the trailer inside a garage…
(1) You won't be able to use propane
appliances inside an enclosed space, and that includes the HW heater. Some are 2-way; many are LP only.
(2) In some places the lease terms or local codes may prohibit what you're planning to do. A night here and there, and folks might look the other way, but more than that could raise eyebrows.