Respectfully, 40 hours a week, plus extra on top of that, is normal for a traditional student, but not usually for a homeschooled child. Furthermore, many homeschooled children, in general, spend the majority of their "school time" as family time, as they are typically being taught by their parent(s) alongside their siblings. For as many homeschooled children who are taught in a traditional-type setting at home, there are just as many (if not more) who are being educated in a non-traditional style. You're making a huge assumption about the OP's homeschooling regimen, unless I missed something as I read through this thread.
In response to the OP...
DH and I are very much the decision-makers in our family. We work very hard to provide a comfortable life for our family, and we are the ones who decide how our money and time is spent. With that said, we have learned through the years that compromise works very well in life - not just with the family, but in real-life situations outside of the family. Life, in general, is not black-and-white - it is comprised of many shades of gray, requiring a certain degree of flexibility to achieve the desired results. In a situation such as yours, I really think that compromise is essential. Contrary to a seemingly popular belief, compromising and "giving up authority" are not one in the same.
As with many families, the older siblings tend to have some responsibilities in helping with younger ones. I think that's very normal and very healthy. I also think it's really important that the older siblings are given time to themselves, without having to be responsible for their younger family members - they are children, not parents, and they should not have to play the role of another parent in a family. (I'm not saying that is what happens in your family - just making a statement.)
Giving a teenager a little autonomy helps to build good decision-making skills and increases self-confidence, while allowing them to feel that their thoughts, feelings and opinions are valued. By giving your child a choice - and it should be options that you are ok with - you are giving your child the opportunity to think for himself, make choices for himself, and live with the natural consequences of those choices. If he chooses to stay with his grandparents, he could end up having a wonderful experience with important family members. He could also end up regretting making that choice, and that's an important life-lesson, too! Since you asked... DH and I would give our 14 y/o a choice to either go on the trip with a good attitude or stay with the grandparents. We would be ok with either choice.
Ultimately, you are "in charge" of your children... make him go or don't; that's completely up to you. I will simply say that you will get much better results in the long-run by leading with a firm hand and a soft touch, than you will with ruling with an iron fist.
If you're interested... there is a difference between being an Authoritarian Parent and an Authoritative Parent. Also, an Authoritative Parent is NOT the same as a Permissive Parent.
Sorry for the lengthy post! Good luck!!!