There are a few UNO's to choose from, but none are within walking distance of Union Station and would require either taxi or public transportation to get to. The closest one to Union Station would be at 29 East Ohio Avenue. However, if you want true deep dish pizza I would suggest Gino's East pizzeria located at 633 North Wells Avenue.
Now I do want to caution you that your train, the California Zephyr, leaves Chicago at 2:10pm and should be at Union Station an hour ahead of time at 1:10pm (espeically since you have children and will qualify for pre-boarding). Gino's and UNO's will not open until 11:00am or 12:00pm and you should leave atleast 45 minutes to get from the restaurant to Union Station. So with time constraints you may want to skip the pizza this time around and just hit the museums. Now there is a fast food deep dish pizzeria located in Union Staton, but I've never eaten there myself.
Personally, I suggest the Feild Museum over the Shedd Aquarium. The Field Museum is much more kid freindly, hands on, and, in my opinion, a lot more interesting. In order to get from Union Station to the Museum Campus (which is the locatation of both the Shedd Aquarium and Field Museum) you want to take the #28 bus from the corner of Jackson and Canal.
Enjoy your trip. B)