First off, I think you are brave and correct to say that if you are going through some issues in your marriage, it may be effecting your son's behavior. Kids see and hear a lot more than we give them credit for and they don't know the 'right' way to react to that information- so they act out somewhere else like school.
You mention that your son went to a private christian school for preschool. The routine there, curriculum, etc. may have been very different from his current school and he may be having a difficult adjustment- but that doesn't mean to give up on the school OR to blame him entirely. But it could definitely be a factor.
First off, ask for a meeting with the teacher. All the kindergarten teachers I know are really just amazingly sweet people who want nothing but to give their kids a great start in school and teach them to look forward to it. You don't say specifically what the issues with your son are, but if she has say, 15 kids in the class and your son is the one causing the issues, she is doing the right thing to contact you now and try to 'nip it in the bud'.
I don't know that punishing your son will do much good at this age. I would work with the teacher and talk to your son and try to figure out WHY he is misbehaving- especially if he was not doing so in preschool. Is the new work too hard or too easy for him? Does he miss his old friends? Or is he just a fidgety little boy (perfectly normal!) who is having trouble paying attention, etc.
Most kindergarten curriculum is geared around 'fun' as much as learning concepts. See if there is a particular subject your son IS paying attention to and learning well and talk to the teacher about why she thinks he is doing better with some things than others. Try to use the same approach for other things as well.
If they are just behavioral issues, you need to just keep repeating the Golden Rule of 'do unto others' to your child and ask him things like " Do you think Susie liked it when you pulled her hair? Do you think it hurt? How would you like it if she did that to you?" Use actual incidents and talk through them to get him to understand WHY he should not do whatever it is.
Most of all, keep the lines of communication open between you and the teacher. Be informed and if you are all acting together, I bet your son will adjust. This is a big change for him- hopefully he just needs some time and a little more supervision from you and your husband! Good luck!