Authorship of an article based on semester project
What is considered normal, hence ethical, varies by field. In mathematics, this would be a highly unusual situation. But in some lab sciences, the PI is normally included on all publications since the lab itself exists only by their efforts. 

I suspect you are in some such field and would then suggest that the senior professor should probably get his way. It may even be advantageous to have him as "corresponding" author as it may ease publication. In such fields readers understand these things and know who does the actual work. Thus it isn't considered to be a problem in those fields. 

If you are a co-author it is probably as much as you can expect here. And maybe even that is impossible. But work to get an acknowledgement in the work, at least - especially if it says that the original idea came from you. You actually say that the student did the work of developing the idea, of course. If the student is "first author" it is a good outcome. The rest is just a bit of an arcane dance. 

I think that if you don't press to hard for what might be considered in the field to be an unusual outcome that the relationship between the student and the senior professor will settle down sufficiently.