So your son is 5 and this is his first significant experience being away from you? And it's full day? That's going to be a hard transition. (Not saying he should have started earlier, but it does mean it's not a 'quick fix'.)
I think there are two separate issues:
1. The drop-off issue. This is true 'separation anxiety' in that the thought of being separated from you is what makes him anxious. It's not being there, it's the actual act of leaving you. That's pretty typical. It's also very typical for it to surface after the novelty of daycare/school has worn off. The first few weeks it was fun. Now it's just school. Our ds is pretty reserved and started daycare 3 days a week at 2 1/2. Until he hit about 4 1/2, he didn't like to separate. This will get better. Things that helped:
-Arriving early so that the classroom was less busy and the teachers had time to tend to him.
-Handing him over to a teacher (not trying to get him interested in an activity).
-Being quick but loving.
2. Missing you during the day. This too is pretty typical. I'd only be worried if he keeps this up for a number of months, and if it's long bouts of crying and not just a "I miss my mom" kind of thing and then he moves on. I'd ask the teachers about this (maybe via e-mail so he's not overhearing it). Ask if they think it's interfering with his day. Ask if they think it's atypical for a child who's not been away from home much before. Ask what they do to comfort him. For our son, the teachers used to help him write letters to me and that gave him some power over his feelings. Heck, I even got a few of those from our daughter, who never showed much separation anxiety, in Kindergarten (it too was Reggio Emilia and all day). Kindergarteners do miss their parents.
I would recommend therapy for you (first), and then maybe couples therapy. You need a 'neutral party' to talk about issues such as: Why do you feel so strongly about homeschooling? Why is this (relatively normal, but distressing behavior) causing you so much anxiety? Is there a way you can come to peace with your compromise? Why, if you feel so strongly, did you feel you had to 'give in' and try school with your kids? Is there any way you and your husband can work through this difference that feels right to both of you? Those are some pretty big issues.
Honestly, I don't think your son needs therapy right now. I don't see anything concerning in his behavior, but the fact that you're crying a lot and you're constantly tense over this issue is not good. And he could be picking up on your tension. Kids have a great sense of when something is off with their parents.