during one pool session. I tried for about 10 minutes to pee
I do hope you're joking? Peeing in the ocean is one thing. Peeing in a swimming pool or even in a freshwater lake is quite another.
As to peeing just before you get out, I tell my students that when they pee (I know they will) to do it at least 10 minutes before they get out, to allow the pee time to dissipate from inside their suits.
I have friends who say that if you don't need to pee during a dive then you're not sufficiently hydrated. Especially with more demanding dives in cold water. One male friend, with a drysuit suitably equipped, let rip during a long trimix dive in rather cold water. Unfortunately it was so cold that the condom-part of the device was not sufficiently tight and slipped off.
Two things then happened. Firstly, he really needed to go very badly and once having started he couldn't stop. Secondly, the knob on the outside of the suit which seals the whole device from the outside water during most of the dive was of course unscrewed, and he was so concerned with what he knew was going on that he omitted to close it.
He continued with the dive, distinctly damp. At the end he surfaced but had so much water in his suit that he was too heavy to raise himself onto the ladder. So he removed all his gear (which was taken onto the boat) and enlisted the help of other divers in the water to unzip him and help him out of his by then very wet "dry"-suit. I was on deck at the time, but I understand they found the aroma distinctly repellent. He was obliged to remove his inner suit in the water as well, and both drysuit and Thinsulate were tied to ropes and left in the water while he climbed up in his underwear, which had effectively been rinsed clean.
He was then responsible for recovering his suits and washing them with detergent in a large rinse bucket on deck. Only once they smelt OK was he allowed to take them into the engine room and hang them up. Sadly the liveaboard was a converted trawler and didn't have effective drying facilities, and he dived for the next three days in wet clothes.
I've lost touch with him, but I'm sure he has taken great pains not to do that again!