You're still her mother--can you not talk to your youngest daughter and tell her to behave herself during the drive?
People are right--etiquette does not ever ask the hosts to do anything more than host.
Hosts aren't even supposed to run around lining up other drivers.
Guests are supposed to be grownups, who ought to be able to get themselves to anywhere they need or want to go.
So invite them, and don't say anything about transportation.
If one of their strategies for getting where they want to go is to ask favors of friends and family, they can do that all on their own. They're grownup enough to live independently--they can ask for favors, etc., all by themselves.
Of course, individual human beings also have other conversations, so it's possible one of them might ask you for help, or for suggestions. That's quite apart from your role as a host--that's your role as a family member.
And if one of the daughters wants to call Grandpa and volunteer to drive him, she isn't required to call her sister and make the same offer, even if Annoying Sis does live in the same bldg as Gramps.
That daughter might run the risk that Annoying Sis will get mad--that's on her. But you shouldn't be interfering in the relationship in that spot by taking Driving Sis's side. (I think it's OK to interfere by telling Annoying Sis, if you hear about the problem, "well, perhaps you should consider why she doesn't want to offer the ride to you." and any other observations, such as, "I hear you constantly saying rude things to her--what did you think would happen?").
And if Annoying Sis won't get a driver's license--well, that's the price she pays. If she doesn't want to pay that price, she can go get a license. (I will say that I'm reacting a bit based on my BIL, who announced that he wasn't going to get a license, bcs he thought it would be too hard, he didn't want to drive in the city, etc. My response, "OK, but it's really out of line for you to expect to be chauffeured everywhere you want to go then. Esp. when you're assuming my DH will drive you late at night, etc., AND drive back." Maybe your Annoying Daughter has a medical reason not to get a license, or something. But that still doesn't absolve her from the responsibility for arranging her own transportation.)
I actually think that once kids move out of the house, parents should NOT be taking the initiative to arrange transportation, etc., for them.
also--difficulty getting up the steps of a bus is not "unable"--Granddad can surely withstand a small bit of difficulty. I don't know where you live--most cities in the US have buses that are able to help elderly or disable people get on them.
I get that doing all that driving is the best way to get what you want, but honestly--these are grownups. Tell them that this party is REALLY important to you, and you REALLY want them there, and let them figure it out. Or at least make them participate in the discussion!!!