Your 21 month old isn't even 2 yet. This is absolutely no surprise. Even at 3, children do not really play together, rather, they play side-by-side. I would not enroll my child in any kind of pre-school prior to age 3.
My 4 children all went to daycare from 6 to 8 weeks on, so they learned that Mom and Dad left them, and returned again, and they lived in a world with other children. Even so, at 2 years old, an environment without their primary care giver (you or the daycare person in our case) would be a challenge.
Play groups are okay, but maybe you should stay with your child in the play group until he is comfortable there, and feels the location and people there are safe. THEN, you can try leaving again.
When we moved to our current home, I became a stay-at-home mom for the 1st time. Our youngest was 3. She had been in daycare all her life, but when we took her to church, she wouldn't let me leave her in her Sunday School class which was team taught by a mom and dad. I stayed in 3 yr old SS for about 3 months until she felt safe there. At that point, it was kind of exciting to go to an "adult" class and get to know my peers. Other options? If you want to go to the moms group, and your child doesn't feel safe in the day-care part, do you have a family member who will babysit at home? I wouldn't force my child out of his comfort zone when it is unnecessary, and when it will be a whole lot easier at a more mature age. Even 6 months will make a big difference in your child's development.
In preparation for separation from Mom, does he go to visit friends whose moms are your friends? So he's used to going to different places and being with other kids with Mom present? I would start getting him used to that, rather than expecting him to have you simply walk out and leave him where he is. Young children do not have a conception of time, so when you say, "I'll be back soon," he only knows you are leaving him.
Another good thing to do is to play peek-a-boo. Believe it or not -- peek-a-boo reinforces the idea that you still exist, even when he can't see you. If you can find children's books that deal with topics like going to pre-school, or play group, or whatever -- things that might cause anxiety for your son -- buy those, and read them together. Read the books before you buy them, however. You want to be sure you approve of the message - just because they are childrens' books and have passed through the publishing editors does not make them good books. :-)
Above all -- no matter what else you do -- ENJOY your son. Make sure he also knows you enjoy him. He's gonna grow up, and in 4 years he'll be in kindergarten and you'll be wondering where the baby went. It's hard to believe, and you never quite can conceptualize that until it happens. Try to slow down, relax, lower your expectations a little, and simply enjoy having him in your life. Parenting can be incredibly frustration, but it is also a source of great joy and love. You and he will both get there !
My best to you on your journey !
barb
Regarding discipline: I think you are right on about the time-out thing. He is petrified every time to leave him alone, and if you did a time out thing, I don't think it would work. I usually gave whatever order I was giving, and counted to 3, often re-issuing the order along the way. When the child didn't obey at 3, then I simply walked into the situation, held my child, gave the order and forced compliance (gently). The child understands that he can do it himself, or you can force him to do it, but either way, he WILL do it. I think that's more effective because you get the result you want without having to get angry. Obviously, in a dangerous situation, you move in as soon as you give your command, but for everyday behavior issues, help your child to WANT to obey you, by reinforcing the good behavior, and forcing the required behavior, then hugging when it's done, rather than making a big issue out of disobedience.