Here is where the ambiguous terminology is a real problem. You say that part of the road is a private road and part of it is a private way, and that those on the private road have no right of access on the private way. Where did you get the terms private road and private way as applied to the two sections of road? Is that what is says in the subdivision plans?
According to 23 MRS 3021, a "private way" is the same thing as a "public easement," and "public easement" is defined in sections 3021 and 3022 as providing public access to land or water not otherwise connected to the public road system, and is for access by foot or motor vehicle. So if you go by that definition, those on both sections of your road have a right to use the part that's a "private way," but those on the "private way" do NOT have a right to travel on the section that's a "private road," because that is indeed private. They would have to have deeded easements over the "private road."
On the other hand, title 29-A section 101 paragraph 58 defines a private way as, "a way privately owned and maintained over which the owner may restrict use or passage." That definition is pretty much the opposite of the previous one.
But definitions and terminology aside, as far as your road associations go, let's see if I've got this right. If I'm picturing this correctly, as you enter onto the road from the public road, those in both subdivisions have the right to use the first section of road. But then it transitions to a second subdivision, and those in the first subdivision do not have a right of access over that section of the road. If that's correct, then those in the first subdivision could form a statutory road association and include the members of both subdivisions because they ALL benefit from use of the initial section of road. But those in the second subdivision could not form a statutory road association and require those in the first subdivision to be members because they do NOT benefit from use of the second section of road.
Both sections of road could therefore have one statutory road association so long as it's formed by those in the first section, i.e. I believe the three people who sign the request to the notary would have to be in that first section. They would then have to notify those in both subdivisions because they all benefit from the first section of road.
Then the question is, do the people in the second section need a separate road association? My guess is that, "that depends." The first section could have something in their bylaws and/or in their formula for assessments that makes it "fair and equitable" for both subdivisions. That is, the people in the first section should not be obligated to pay to maintain the section they are not allowed to use. So those in the second section would pay a higher fee because they use both. If it were all one road, more likely everyone would pay the same fee, even if they rarely have occasion to use the whole road. But since they are not even allowed to use the second section of road, there could be valid objections.
Another possible solution would be to have two separate road associations, one including members of both subdivisions, and one including only the members of the second subdivision. People in the second subdivision would therefore pay two fees, one to each association. The end result would be about the same, except when it comes to how much control the voters in each section have over any decisions made as to how fees are charged or funds are spent.
I've also heard of situations where each association does all the collections from those on their section of road, but the second subdivision chips in an agreed upon total sum to the first association for their collective use of the other association's section of road.
I think the main thing here is to get as many as possible of the members of both subdivision together and discuss the options. If there is already friction that indicates that might not go smoothly, I would suggest getting a professional mediator to help. There are some who regularly do group mediations, and they excel at getting people to listen to each other and find mutually agreeable terms.