I would call the Head Start program and ask what the options are so that you have the info. At the preschool and elementary level, however, the kids are not "sitting through" 6 hours in the sense of being confined to a desk. It's pretty varied and there are many modalities used for learning and special services (speech, OT, etc.)
I am a stepmom so I understand the difficulties in trying to work out shared custody and all that is involved. You must resign yourself to a certain amount of driving given the distance between the two homes. That's what we sign on for when we marry men with children. However, I think Penny's response is a little over the top. You are trying to get info and that is reasonable. You gave no indication that you are discussing the problems with his mother in front of him, so I'm not sure where that issue came from. I DO agree with her, though, that it will be better for everyone, including you, if you let (or insist that) your husband take over these matters when it comes to making arrangements. He and his ex have to deal with each other at least until this little boy is 18, so they might as well start now. Also, there are a lot of reasons why the child may be "a little behind" and there are many services available. It might not be due to her negligence! I have 2 stepchildren from a pretty horrendous mother whose choices have had a terrible impact in many ways. I've been on the receiving end of having scheduling problems thrown at us, so I know how you are feeling. However, if your husband has shared legal custody (which he appears to have, since he has shared physical custody), he has an equal say in which days the child goes to a program, and which program. Let him and the ex handle it, using the divorce agreement as a guideline. The more of a back seat you take now, the easier it will be for you - I know it is so hard to stay "uninvolved" with a child you love and care for, but Penny is right in saying that the dad has to be the one who takes the lead here. He should call Head Start himself if he can - otherwise you should JUST help with the information gathering, as you are doing.
Good luck!!