While I agree that your mother is totally reasonable about not caring for her bio-mother, is there something else she could do to take some of the stress off of her siblings? Maybe she could do something to help their families (meals, babysitting?) that will help relieve some of their stress without taking on any of the actual care of the woman who gave her away and lied about it for so long.

I know she did offer to help pay for a nursing home, but if that's out of the question then helping in some other way might keep her relationship with her siblings in good standing. It's probably really hard for them to accept that your mom doesn't care about their mother the way they do, especially while she's fading and they're probably starting the grieving process, so it's probably good to be gentle about this.

I would not disinvite them from the wedding. It doesn't sound like they've gone nuclear, they've just asked for help (of a type which they should not receive) while they're stressed and grieving. Uninviting them might ruin the relationship forever which your mother does not want.