It seems that the exact meaning of between is very tied to its specific usage. What should I assume in a general situation about the inclusivity of between? Consider:
"Pick a number between 1 and 10." Most people would consider between inclusive.
"How many numbers are there between 1 and 10?" Most people would consider between exclusive, i.e. 8 to be the correct answer.
Could the meaning of the word between have something to do with the grammatical structure of the sentence in which it is used?
There is no rule as to when between can be considered inclusive or exclusive, and the grammatical structure of the relevant sentence would not affect this.
You may be able to make deductions or assumptions from the subject and context of the sentence itself or surrounding sentences, but that would be only assumptions.
If the question of inclusion or exclusion were critical, the only way to determine what was intended would be to ask the author or speaker.
Personally, I would say that very strictly the limits of "between" are exclusive. But you cannot tell how any particular person uses it, and therefore, the only appropriate answer to your question is: "If in doubt, ask!"
Addendum (post-acceptance): The fact that "between" is strictly exclusive of the limits can be illustrated by considering its use when referring to physical objects. For example, you might refer to:
the gap/space between two parked vehicles
the path between the river and the road
In such cases the 'limits' are the vehicles, river and road: "between" does not include the vehicles, river or road, but refers only to the 'area' within those 'limits', namely the gap/space or path.
Likewise, "between 1 and 10" excludes the 'limits' 1 and 10, and includes only the 'items within those limits, namely 2 to 9.
As TrevorD says, there's no reliable way to tell unless the speaker actually says "inclusive". In US English there's the useful form "One through ten" to indicate that it's an inclusive range, and it's making some headway in British use. That's one American language import that I don't mind, because it's so useful.
Like in the example above: which is the distance from the river to the road, it surely must be exclusive (unless you are on the wrong side of the river, in which case you might be asked if you want to include the width of the river). So from....to also requires context. Right?
