Is it obligatory to invite partners of the bridal party?
It may not be the answer that you want to hear, but if they have been together for a while (say more then 3 months) then the answer to that would be Yes. In fact I would find it quite rude if I was a member of a bridal party and my partner was not invited.

Alternatively I could use his sister, he could use his brother as a GM but then my brothers will be left out.
To me this would be the best solution, especially if you get on reasonably well with your future SIL. As to your brothers missing out, if you explain to them that by having the flowergirls you are incorporating "your side" surely they would understand? They could be included in another way, ushers at the ceremony, handing out order of service booklets at the ceremony or doing a reading.