B.W.
Age 2 is young for preschool. Even at 3, children do more side by side play than real "playing together". He is in a new environment, and it's structured and he's not used to that. I think he's kind of young to participate well in preschool anyway, esp cuz he "just turned 2". If you really want him in preschool, I guess I'd go to the church one because it's a smaller group and he does better in the smaller group.
You might also consider going to Sunday School with him, so he has an opportunity to be with other kids on a weekly basis. But I'd drop the larger group because he's not participating and your getting frustrated. If he were 4 and having these issues, that would be different, but he's only 2. I don't know what the ages of the other kids are, but I didn't put my first child in preschool until age 3.5, and even then she didn't talk to anyone there for 2 weeks, and she was a magpie at home. . . my next 3 children never went to preschool because they had been in daycare since birth, and were getting interaction with other kids there. All my kids have been good students, 2 are adults with active and fulfilling jobs, and 2 are in high school, one in a magnet school with a competitive agenda, and the other in regular public school. I think it's important for them to have those early years to develop at their own pace without a whole lot of pressure to excel or be something they are not.
If you are concerned about behavioral issues, talk to your son's doctor, or an early childhood educator to find out what age-appropriate behavior is. I think he sounds like a 2 yr old, frankly, but I'm online and not there in person to witness any of this. :-)
If you decide to pull him out of the preschool environment, don't think of it as a failure. You tried the preschool thing, it didn't go well, you amended the plan. It's not a failure. Perhaps something different would work better -- like going to the Y for swimming or something ?