To find the difference, we need to subtract the distance from the library to Town Hall from the distance from the school to the library.
Distance from school to library = 3 1/2 miles
Distance from library to Town Hall = 1 1/4 miles
Difference = 3 1/2 miles - 1 1/4 miles
= 14/4 - 5/4
= 9/4
= 2 1/4 miles
The school is 2 1/4 miles farther from the library than from the library to Town Hall. Answer: \boxed{2 \frac{1}{4}} miles.