Mametchi always grows up when there are 0-1 care mistakes, so guess you're not making any care mistakes. Not taking the toddler to the bathroom doesn't count as a care mistake (you can have 6 poops on the screen and they won't trigger a care mistake at all).
Care mistake happens when you let your tama get either it's hunger or happiness meter empty and calls you to take care of it, and if you ignore it for long enough (I think 20 minutes), the attention call icon turns off- that's a care mistake.
As for Prince Mametchi, he isn't a special growth stage. He is a Henshin Jo change. If you give him a crown and take him to the Henshin Jo place he will change into it. So no poop shenanigans are needed for him, if that's what you mean.