Note that the TSA website explicitly allows ice packs if they are to keep medications or baby items cold. You may even want to print out that page in case you run into a group that doesn't know the rule (as we did at LAX).
We also have 1 and 3 year olds and have had no issue with milk, juice boxes, sandwiches, fruit. Haven't tried yogurt, honestly. Tend to get more pushback from the smaller stations (CMH, CLE) than the larger ones (SFO, ORD, ATL). Not a trend, just my observation.