You had better review that with your BA before proceeding.
A call in is fine. But the grievance would not fly here, and would only make the company, and the union set you straight.
The local and the company have undoubtedly dealt with this situation before. (senior employee has to change an unpaid request off to a paid day off to bump a junior employee's paid day off request).
Seniority in nearly all cases will be respected by the Union. The unpaid day off request by the senior employee will be viewed as conditional...If he needs to burn a paid day to claim the seniority right to the day off, he has the option. It is the way most centers work, and frankly it is the way that respects seniority. So a grievance would, at the most, formalize the local request procedure (management will then be required to ask every senior driver with an unpaid request off submitted if they want to change it to a paid before a less senior driver gets a paid day). This is probably already the case since your sup said they will make him burn a paid day. But the grievance will not result in the less senior driver getting the paid day before the more senior driver.
At the same time, by filing, you will be seen by the union as a guy who doesn't respect seniority, and by the company as someone who creates headaches for no reason.