T.G.
Hi S.!
For starters, good job. You're doing great. Sharing is a skill all kids need to learn, and your son is learning it now - that's his job right now, is to learn how to do this - and to find out whether if he screams just a little louder or longer, the rules will change. So good job being consistent and keeping the rules firm. And good job getting him into child care - his transition and socialization into school would only be harder if he were home with you all the time, and he wouldn't learn these things as easily. So I hope you feel good about what a great job you're doing!
I've heard good things about the Karp book, 'happiest toddler on the block' so perhaps you could give that a try. I worked in childcare for several years, and toddlers were a challenge in this way. But here are a few suggestions I picked up from those years, take it or leave it:
--give him some warning when you're going to take away a toy or transition to a different activity. "you have two more minutes. one more minute." etc - and then stick to that - perhaps even buy a timer, and when it beeps, it's time. don't keep adding time, though - let the deadline be firm. But tell him when he can play with it again/do that activity again "Oh, would you like to play with this again after lunch? Sure, you can play with it after lunch! Where would you like to leave it while you're eating?" etc.
--if he screams, you can validate his feelings by saying something like "I hear that you're angry. It's OK that you're angry. would you like a hug, or your blankie?" something like that. after all, these lessons aren't easy for him. Or you can say "if you're angry, say 'i'm angry!'"
--but if he's throwing a tantrum, he can't come sit at the table or have some other desirable thing until he can calm himself down. and you can affirm his ability to do so: "you can calm yourself down. calm your body down." sometimes they aren't even aware that they CAN control themselves.
--give him choices - no more than two, though - so he has a sense of agency. "would you like to put that away by yourself, or do you need me to help you?" wait a few seconds - not long! - "ok, i see that you are choosing to have me help you! I can help you put it away." and take his hand and force him to put it down/away/whatever. also works for "helping" toddlers to move to a new area (lunch table, etc). If he does do it, you can say "oh, that's great! you decided to do it yourself! good job!" or something affirming.
--as for sharing, the timer works well for that - if you want to help him practice sharing, pick up a toy he likes, and when he wants to grab it tell him he can have it in two minutes. set the timer for 2 minutes, and then give him a 2 minute turn. so when the timer beeps it is your turn again.
again, these are just things we did at the day care center i worked for, but they did work well in the toddler room. i hope you find some things that work for you! best of luck!
sincerely,
T.