I know it is really hard when intellectually gifted students are young to watch how the school cannot meet their needs. Hopefully, you can call your GIEP team together and add what your student needs, sooner rather than later. There are so many people on staff in one school and throughout a district and even a county, that there may be someone other than that one teacher who could or even would love to work with your student. Perhaps even someone studying teaching and / or giftedness in your area might be available.
As far as the difference of opinion between spouses, the good news is you are not alone and here is my opinion of why. Very smart people like to partner with very smart people. They have very smart children. Of course you are both going to have strong opinions and those opinions might clash. Both parents care so much about the child and the child's education, combined with gifted persons' predisposition to being intense (in a good way), then you can really feel temporarily at a checkmate.
I would talk to everyone involved in the process from superintendent to teacher's aid and find the solution. You will feel better knowing you did everything you could.
Here's one point I contemplate. Society benefits when gifted people 'do their thing' in their chosen professions, but when we bring that same passion to advocacy for our child, they just don't see it necessarily in a positive light.
I can tell from the response posts that everyone feels your pain and hopes that you hang in there and know that you are not alone. It helps me to remember how great it felt to break out from the pack and be free with electives and choices. That time will come. It's just that still today the overall education perspective is to hold these kids back until they are older. You are not alone.