You can screw some 2x10’s or 2x12’s into a square and put it in the yard or the garden. It can be easily picked up and moved for grass cutting or if your parents want it moved. Just make sure they can’t escape from underneath.
Did you let him go or did you retrieve him? I get confused easily though.....
If the pen is just for exercise, I would think moving it wouldn't be an issue for your guy but if you want him to breed, I would think a more permanent home in the corner of the yard that doesn't move and doesn't cause stress would be your best bet.
As someone else mentioned, 2x10s make good walls, 2x12- perfect walls. Just run a couple of boards over lengthwise to provide lateral cover from the sun.
I like to make sure, positive sure that a good part of the pen has shade at any point in the day somewhere in the pen. The last two I built were under Boysenberry trees with the berrys providing a nice snack for my guys.
Parents.......yeah, they kind of want to keep the yard for things they like, not always what kids need. I would suggest that you take all the persuasion skills you have learned and put them to work on the easier of your two parents;
Reasons to keep pen in one location;
1. You won't ever trip over it b/c it will be in the corner of the back yard.
2. Aren't you "woke"? Animals need a permanent home too.
3. It won't look bad in the corner, I promise.
4. Turtle pens never need to be cleaned(white lie) and never smell!!
5. Studies show that children with pets excel at social skills, math skills and most importantly, RESPONSIBILITY.