ok, yes i would insist on it. Specifically looking for giardia.
There aren't many things that will make a glider throw up, it's a symptom of only a couple different things and the way his poop looks I would look heavily at parasites.
i'm going to ask a few questions please answer as thoroughly as you can, no details are to small. I am not asking to judge , but if he was constipated that is usually food related.
What diet are you feeding, please include everything you put on the plate.
What treats are you giving, please include everything you give them.
Enlarged bladder, did they test his urine?
What kind of water do you give him