You may already be finished up with your trip, but we live in the area. I'm not sure about dance sessions anywhere, but Pleasant Prairie is a beautiful facility. My daughter just did a competition there this last weekend.
Glacier in Vernon Hills is maybe 30 minutes from Antioch, it's been awhile since we've been there so I'm not sure on ice quality. They have two sheets and a big synchro program.
Leaf's is pretty far from Antioch and expensive, but an impressive facility with 3 sheets of ice and a humungous lobby.
Probably a good 45 minutes drive from Antioch is Triphahn Ice Arena in Hoffman Estates. They take good care of their ice (at least the last time we were there) and if you go for a weekday lunchtime public, it is cheap and empty. Daughter doesn't skate there anymore, and we miss the facility.
There are a slew of rinks in the North Shore area, along with synchro teams, so you might find a dance session at one of those rinks but I'm unfamiliar with them. We have been to Skokie Skatium a few times and it was decent. I know of somebody who does ice dance and I think he skates out of Centennial in Highland Park, so maybe they have a dance session. Another friend of ours skates at Robert Crown in Evanston and they like it there. Have fun!