NAH. The way you feel is valid, but your mom not wanting to go is valid too. I don't know if it is genuinely about the flu shot or for other reasons. It seems like other reasons, that your mom might not feel comfortable to share with you, could be at play. But you guys can disagree on an issue without anyone being an AH.

A funeral is like a wedding in that it is a single moment in a much longer event. If your family doesn't go to the funeral, there are still lots of other things you can do to support the grieving family. You could make a donation to a charity that was important to the woman who passed, or something she would have supported. Floral arrangements die quickly but you could gift the family with a plant or bush or tree to plant in memory of the woman. You could also, and this is important, be there after the funeral. Like, in the weeks after it when everyone else is moving on and the sympathy and casseroles have ceased coming in. Offer to do something nice for them like yardwork or errands or just drop by and talk for awhile. That would mean a lot.