I know you have received many suggestions, but I do have a few more.
First, for ice cream, a very old town, famous ice cream place is tiny and cramped, but the most amazing place. It is called Margie's and it is at the intersection of Milwaukee Ave, Western Ave and Armitage Ave (a six corner intersection). It has the best ice cream, home made fudge sauce, and old fashioned decor. Not an experience to be missed.
Margie's Candies
1960 N Western Ave
Chicago, IL 60647
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Also, a more relaxing way to spend an afternoon is down at the beach, which can be walked to from Lincoln Park Zoo. My 8 and 10 year old girls love to just wander the beach collecting things, but swimsuits are even better. What a way to unwind, instead of racing around the entire trip.
Also, they rent multiple person bicycles on the riverfront and I am sure you could get one for the three of you.
I hope you enjoy your vacation! I lived there for 12 years of my adult life, moved back to my hometown of Peoria a couple years ago and really miss Chicago. It is a wonderful place to be!
I agree about the museums and your nine year old. She will enjoy the children's museum on navy pier probably much more than the others. It has mostly interactive exhibits. My kids love it there. It is also a great place to catch a boat ride, and there is the huge ferris wheel. Many shops, including Haagan Daaz, yummm.
Also watch for the free trolly's that go between some of the attractions.