Hi @Cristina,
I guess that like most other posters, my question is about whether your 3.5 year old is ready for this. You're on the cusp, and it depends a bit on the individual, and how much is being carried. The
Sprout was designed for kids between the ages of 4 and 8, according to the linked blog article, and sometimes there's also the attraction of particular color (I'm thinking of @dorayme's
finding a Punch colored original design Side Effect for her daughter, then 4 going on 5) to provide an incentive.
My other thought is that, as @threads remarked, do not give them items that are easily "detached" (e.g., even if a Small Shop Bag is light enough to easily carry, it's too easy to put down and forget!, while a backpack or a bag that is attached via a waist strap is more likely to be identified with as "theirs").
By the way, I do like the design of the retired Sprout for kids -- even if the size is not optimized for carrying A4 binders (but OK on notebooks).
I'll just say that some of the best posts (and later, pictures) about traveling with kids who have their own bags have come from @Toblerhaus, who started a thread
International travel bags with kids back in 2012. (Her kids were 7 and 9 by the time of her post, but they'd been traveling with their own bags for a while. They later got their own Synapse 19s -- and I was frankly envious of the individual pillows that she sewed for them that showed up in the detailed later packups.)
I'll just point out that while it is more understandable that your child would take off a backpack while in a library, provided there are not really long waits due to late rail or bus connections, that might be less likely for your day trips. (And yes, I know that delays can happen on commuter rail lines.)
Good luck!
moriond