I have been legally separated for over 2 years. I filed for sole temporary custody of our children at the time and received it. He has visitation with our children for 2 hours one week and 10 the next week, essentially visitation every other weekend.

We are finally at a point where we have a court date and he is now requested joint physical custody. Our children have been in one home (mine) consistently and are happy and well adjusted in their current situation. What are the chances a judge will grant joint custody?

If he has been keeping up with his visits and so forth it is very likely he could get joint custody. Basically that means you are to inform/include him in decisions concerning the kids.
He may likely get the visitations adjusted if he requests too. If you are uncomfortable with that for legitimate reasons you need to tell the Judge your concerns and they will take it into consideration in the decision if they feel it is important.