Ours is a singleton and our first. We had pressure to have him fully potty trained for pre-school, which he started in January at 3 years old. The pre-school will only go as far as to escort kids to the bathroom, and isolate them from the others until a parent or guardian comes to put fresh clothes on a soiled chiled.
He knew how to use the potty, and would do so, largely without balking if we prompted him to do so. He would withhold at daycare, and his grandparents and soon find himself with wet pants. We used stickers and m&ms, we used training pants, and pull ups, bare bottoms and having him clean up. had a 2 week x-mas holiday with him at the end of december before pre-school started, but as he was already going when with me, I don't think that the extra time together helped advance the cause.
The thing that seemed to take was to leave him in control. We told him, when he was in the mood to listen, that he was a big boy now, we knew he knew how to use the potty, and that mommy & daddy wouldn't be telling him to go anymore. If he wanted to, he could use the potty and we would reward him with m&ms. that some prayer and some nailbiting, and he was good to go.
He has been in the pre-school now for 2.5 months, without a single accident.
I don't know if you can glean anything helpful from our accounting, but this is how we got there with our child.
Best,
F. B.