You may need some transition time to get him adjusted. Would the center allow you to stay with him for awhile and then leave for like an hour and then come back to reassure him that you'll be back. Then maybe the next day stay a shorter time and then come back and have lunch with him. He is anxious that you might not come back. Also, is there a way to observe without him knowing?
When I would drop my kids off at the Church nursery I would stay in the hall and peak if they were fussing at first. I would stay until they were settled down, which helped me. At different times some of my kids went through an anxious time and I would stay with them but would leave for a short time and come back. If I said I would be back in 5 minutes, I was back in 5 minutes, if I said 15 or 30 minutes I would return to reinforce that I would come back. This took some time but they eventually adjusted.
Have you ever done playgroups with your son so he has had a chance to play with/near other kids? Or just a park playdate with another mom. Some kids are introverts and don't like being with big groups. It overwhelms them. My son was like that. I found if I could get there early so that he was there and then gradually others arrived it didn't seem to overwhelm him.
You may need to explore your feelings some more. You sound like you would like to get out on your own for short periods but feel conflicted. If this isn't the right situation for your son maybe you could look into other options. Perhaps a family day care where there are only 5 kids in someones home. Or could you train up a mother's helper, like a teenager,to come and play with your son while you are home. If you could find a 12 year old to train up, you would have a babysitter later on that perhaps your comfortable with.
You also need to help your husband feel confident with your son so you can go out occasionally. Discuss with him some strategies for your son and you hubby to bond. Could he take him in the backyard to play for a bit while you pop out. Or could he take him to the park? I would encourage you to find a way here because you don't want your husband to have a lack of confidence in this area. Be sure to give him affirmations when he does do something with your son and things go well. We as moms have to give our husbands some slack sometimes. Remember they are not us and they shouldn't be expected to do things exactly the way we do.
Well enough from me...
Take care and good luck,
LaurieK
www.mymonavie.com/LaurieK