I think 2 times ridden work a day is too much for him. You can ride him a short time like 40 minutes varying the exercices so he doesn't get bored and do some ground work for 20-30 minutes the other day half. As lunging is very demanding for a young horse's joints, I advice you to try other exercises like long reins. Taking him out once more would be good for his mental if he lives in a stable but don't make him work, just walk in halter for a while ;)
I have a 4 years old now, and last year a trainer told me to ride him twice a day as he was getting really fresh. I never liked the idea so I sort of changed the way I was riding him to make the training more interesting for him and this way more "tiring". Once or twice a week I was introducing something new to keep him interested and concentred. I now ride him 40-50min a day, 6 days a week (we alternate jumping, flatwork and lunging) and he's always happy to work and never gets bored.
I have heard of people riding their horse twice a day to control their energy. But I would never ride my horses 3x a day, especially when they are young and still developing their bones and muscles. I would not ride my horse 3x times a day.
Also include a lot of variety and give them rest when they need it. Don't push it. I've seen horses be ruined from being ridden that much at such a young age. They don't need to be constantly ridden. You also should focus on groundwork, manners, and creating a bond.
I wouldn't recommend that much work for such a young horse. At that age they're still developing and learning. It could put more strain on their muscles and bones, and they will because very bored with their work and they'll stop listening to you and be resistant. For younger horses what I like to do is ride them 5-6 days a week. Monday, Tuesday flat work, then I always like to hack on Wednesdays, then flatwork again on Thursday, and if your horse is at that stage or you would like to teach them, jumping on Fridays. And another hack on Saturday. I do that one week and then I'll do Monday flatworm, Tuesday hack, Wednesday rest, Thursday jump, Friday flat. I switch between those two schedules but I adjust to the horse. I normally don't ride my horses (young horses) for more then 30-40 mins per day because I don't want to over work them. And if you do long hack, several miles or kilometres then I would give them the next day off. Sorry this is so long, but personally I don't agree with twice a day or three times a day. I think lunging or a walk in the morning and a ride in the afternoon would work well instead, and teach some ground manners. Hope this helps. Good luck!!
From experience I find that the more often horses are ridden, the more bored they become of their work and therefore they become hesitant and often become more difficult to work with, hence why most riding school horses are 'lazy'.
I usually only ride my mare once every other day to avoid ridden work becoming boring for her. Every riding session is different. If you are going to ride him more than once a day, make sure you're mixing things up rather than continuing with the same exercises to make it more interesting for him.
Riding my mare more than once a day is not something I'd do unless she was overweight and the extra exercise was essential for her health.
I think if that's what your trainer thinks will help the horse than I say do it. Make sure each ride is only like 20-25 min, and include lots of walking after each one so you don't wear your horse out before the next ride. I would space your rides out like have 1-2 hours between each ride.