Sounds like half your reason or more is to figure out how to tow a trailer. You can do that for free, if you know someone to loan you a trailer.
Spending however much per day to rent a TT for 3-4 days to get 1/2 -1 day of camping out of it is not being fiscally responsible either , unless you both just can’t imagine life in a camper for a few days without renting.
It’s a camper. Like a house but smaller.
Finances being as tight as you say, you’ll spend a bunch of money on something you get relatively little return on.
Not sure what you’re planning to get, but for not a lot of money you could buy an older TT, use it for a year or 2 sell it and likely be out less $ than renting several times.
That is if you take care of it and maintain/ repair it. No different than a new one or a rental.