Whatever you do, I would leave the dislike of the fiance out of the discussion. You really can't win on that issue.
There are two ways this can go.
1) this devolves into a fight between you and your brother about not respecting his choice in a spouse. This won't get you anywhere and may permanently damage your relationship with your brother.
2)you keep it simple, you will bf your child whenever necessary. If they don't want you doing that in their home, then you will not be visiting in their home. They are welcome in your house or on neutral territory.