I don't think OP was rude at all.
However, as a mother of a toddler, this situation is close to one that I do find rude--and maybe it's just me. In OP's case, it was a public shopping center where food is sold. Perfectly fine then to eat & shop. I do the same thing with DD (sometimes with food from the store, sometimes with a cracker or something I bring) to keep her compliant during shopping (or she can be a terror). What I DO find rude is if we go to, say, story time at the library, and someone has brought their kid in with food. First off, no food in the library--so even if they do tell their kid it's okay to share, it's setting the example that it's okay to eat in the library (it's not). Secondly, usually they *don't* have enough for everyone and then it distracts my child from what she's supposed to be doing--listening/participating in story time. Obviously, this is a different situation from what OP posted, but I did want to point out there can be a similar situation where the eating of food in public--even if it's the same rationale (maybe the toddler won't sit through story time without a snack?) is quite rude and is disruptive to the rest of the group. (I always have a snack waiting for DD in the car, but if someone else has one during the story time itself, a promise of later food is not very helpful).