I would find a calm cool team member or mentor to meet with the sponsor and go over the issues.
Without going into why or how they achieved this understanding, my sense is they don't understand or buy into what FIRST is.
A) The sponsor needs to understand that FIRST and presumably your team is about change the culture about STEM education.
B) There is a difference between 'sponsor' and 'partner' and hopefully we are grooming a partner in STEM education. It isn't a marketing sponsorship, they cannot use the event as a trade show, or hand out product brochures, etc. 1st and foremost this is a culture changing STEM education activity.
C) They are NOT the only sponsor/partner, NOR the title sponsor/partner, and do not dictate the marketing style guide for the team.
D) Maintaining a team identity is very important to the team, as is the corporate identity to your sponsor/partners.
E) It doesn't help the tee shirt problem but the use of whitespace on graphic displays can solve some problems. We have a big sign that uses whitespace to hold the sponsor/partner logos, as shown here:
http://kellrobotics.org/files/Billboard.pdf
F) It they cannot be moved on the issue, personally I'd vote to return the money and to find a more appropriate partner.
G) When you go looking for new partners make sure they they understand the team mission and how this is truly a partnership.