Is "between A to B" considered good grammar?

Solution 1:

It is not right to use between A to B, or from A and B for that matter, though the former is a common error.

Intuitively, to suggests motion just like from, while between is a reference to two objects and should be paired with and.

Solution 2:

I would say

... between A and B.

but

... from A to B.

Solution 3:

It's between A and B or between Bs.

The dog crawled between us and lay down at our feet.
Traffic was at a standstill between exits 12 and 14.
They had drunk between them a bottle of Chianti.

The NOAD reports some notes about the usage of between.

Between is used in speaking of only two things, people, etc.: "We must choose between two equally unattractive alternatives." Among is used for collective and undefined relations of usually three or more: "Agreement on landscaping was reached among all the neighbors." But where there are more than two parties involved, between may be used to express one-to-one relationships of pairs within the group or the sense 'shared by': "There is close friendship between the members of the club."

Solution 4:

If it is commonly used in Australian English, then it is grammatical in that dialect.

That said, it will likely sound odd in pretty much any other dialect, and may lead your audience to ask whether you have made an error.