The exact same thing happened in my second daughter's school when she was the exact same age. It was a small public alternative magnet school, with one class per grade. Our state has been dealing with chronic education budget cuts for about 20 years, and that particular year, the cut to that school resulted in them deciding to split the 4th grade--moving half into a shared class with the 3rd grade and half into a shared class with the 5th grade. They weren't splitting time like you are describing, but the idea was that the kids would still get the same curriculum in each level. The school arbitrarily made the split, putting my daughter in the 3rd-4th class and all of her 4 other very close friends (this group had been best buddies since kindergarden-3 girls, 2 boys) in the 4th-5th class. It was that, combined with the way I felt that, no matter how hard they tried to make things even, the kids with the higher level co-class would learn more, be pushed more, and develop more than the ones with the lower level co-class. There was no way I was sitting still for that! I called the prinicipal, told her what I felt about the situation, and insisted that my daughter be moved into the other group. They agreed, but reluctantly. It was the best thing I ever did. That 5th grade teacher not only really respected the kids and helped them learn to high standards, the kids respected her and were thrilled to have her for two years!
The group that DID end up having their 4th grade with the 3rd grade class had difficulty and felt separated for awhile when they moved into the same 5th grade class together. They simply had not been pushed and given the higher level of instruction the ones in the 4/5 class had received.
I also drove her across town for that school--though it was a public school, because it was an "alternative" school, the district did not provide transportation. Your child's education is worth anything you have to do. Make them listen to your point of view!