My DS has been diagnosed with constipation as his food intake got down to savoy biscuits, cheese, milk, bananas, strawberries & apple. We were down to doing poo's every 3 days - way too long for a 2 yo. It took until recently for me to realise that he was constipated as TMI sorry he had huge runny poo's rarely solid or if it was would be quickly followed with a loose motion. He drinks loads of water & is not unhappy in anyway. It took reading a post on BB advising that you could still look to be regularly but still be constipated & the fact we had come to an impasse with the TT. Due to not knowing when he'd poo & lack of interest in food. We are seeing a pedatric gastroenterologist. He recommended Osmolax as the laxative of choice as it doesn't cause gas or cramping. Our GP suggested parachoc but we were advised by the gastroenterologist that it does what DS's bowel is already doing & we needed to soften the whole blockage. We had to induce diarrhoea for 48hrs with the Osmolax & it wasn't at all as bad as I thought & the Osmolax didn't work as I thought it would. It set TT'ing back but 2 weeks later he's back to telling us & taking himself to the potty & today he did his first poo on there. His eating had improved. Still fussy but that's part of being a 2yo too lol.
Maybe take him to see your GP & see what they suggest. Sorry for the long story hope it helps in some way. It's hard to spot these things sometimes & doesn't help when day-care is pushing something you don't.
I also suspect that DS2 has a cows milk intolerance as we have since changed his milk to lactose free & having good results. Will see in a few weeks whether it is confirmed or not.