Seems like he is having a natural response to being separated from his known caregivers/family.
Traditionally, kids are not considered developmentally ready for preschool separation until 2.9 years. 18 months is extremely early -- children can adjust to anything but the question is at what cost.
If the issue is to cover the time you are away with your other son for his classes -- can you consider (as someone else suggested) having someone in the house with this son while you are away? There is an immense difference between the attention he will get from an individual caretaker, and the attention he will get in a school environment where there is one adult for 12 children.
Obviously, there are tradeoffs, and you need to do what is necessary for your entire family. But if there is another option, I would consider it until he is older. In any event, his response seems entirely in keeping with a dramatic change in his caretaking. He is not old enough to understand the circumstances, and consequently is feeling the loss of mom and dad's presence in ways that are real (not just anxious or neurotic).
There's also the possibility that the preschool is not giving him the attention he needs, or that there are children there that are hitting or being problematic for him. You might consider sitting in and watching the group dynamics. But I think it may just be the fact that he is not with you that is the problem
Overall, I'm sorry I can't give you more help in managing the stress levels for you both in this current circumstance. I just think it may be too dramatic a change for his age and if possible, other options should be explored.
Good luck with this. You are clearly trying to do what's best for your family, and I wish you all the best.