Learn English – Which preposition is used with tolerance in this sentence

"Of" can be alternated with possessives and adjectives. (quality of approach and variety of sentences) "This approach's quality can be improved by using sentence variation in order to enhance vocabulary and style."

First, “grammatically correct” is not something that applies here. Of course it is grammatically correct. That doesn’t mean it’s sensible — nor that it isn’t. This is not a matter of grammar, but of semantics.

So now for semantics, which is all that ever matters. You misunderstand the semantics of between. Your error is thinking that between A and B only applies in the direction A → B, the way from A to B would. It does not. That simply is not how between is normally used. Between implies a reciprocal or bidirectional connection, so A ↔ B in this case.

This is easily seen in statements regarding shuttle services between two or more locations. For example:

• Complimentary shuttle service will be provided between the Convention Center and official APHA Annual Meeting hotels except for those within walking distance. APHA will offer an extra shuttle route between the Convention Center and the Hilton New Orleans Riverside for easy access between scientific sessions. ^{(http://www.apha.org/meetings/registration/Shuttle.htm)}

• Continuous shuttle service is provided every 10 – 15 minutes between TechEd 2014 conference hotels and the George R. Brown Convention Center (GRBCC) on the following schedule. ^{(http://channel9.msdn.com/Blogs/TechEd/TechEdShuttles#fbid=)}

• Free shuttle service is provided between all terminals and remote parking lots. ^{(http://www.supershuttle.com/Locations/LAXAirportShuttleLosangeles.aspx)}

So don’t fret. Just use between like everybody else does.