It pins when you next use unwrap. Based on the points you’ve selected. But it’s also used to do “live unwraps”.
I have a question for you now. Will the textures associated with the object require any kind of detail? Straightening out edges in an unwrap has it’s limits. This is not something inherent to Blender. If you deviate too far from the original unwrap you will introduce distortion. It’s very dependent on the original shape and how you choose to seam it. Some shapes just aren’t conducive to being neatly aligned.
Having said that, you can get away with it, if the unwrap is similar to the one you have. Which looks roughly cylindrical. Try out UV SQUARES. An older addon. But it might speed things up. There’s a slight bit of stretching if you look closely. But it’s minimal because the initial unwrap isn’t all that far from the actual face distribution of the object. Obviously it evened out the entire selection in my image.
You can use ALT right click to select contiguous edges in the UV mesh. Just as you do in the viewport. If you’re happy with the inner faces and how they look you can just select the outer edges and use W and align on the appropriate axis.
Left of the snapping and proportional editing widgets in the header is a popup list where you can choose what gets selected.
-Shared Vertex will pick A and B, like in your screen shot.
-Shared Location will pick like you want(I’m assuming)
-Disabled will pick only a single UV, and allows you to pull face UVs apart from other faces, but it’s hard to get a hold of the right one usually… A quick WW will weld the ones you want back together.
Nevermind, sorry. The option’s appearance depends on if I have the selection synced to the 3D view. Weird. In 3D Studio Max you “Sync” is on by default but you can control the verts/edges independently. In fact, in Max I’ve never even considered it being out if sync. It’s another feature I took for granted.