You can try to check your gear with a bellman at one of the Hyatt's (2 at DFW). You don't have to go into Dallas. You can grab a taxi. A couple miles north of the BIG airport--DFW--there is a town called Grapevine with a huge outlet mall with some child friendly activities and a Bass Pro Shop that has a lunch area and stuff for children to look at. The fabulous Gaylord Texan Hotel a couple miles from the town (closer to the airport) that has so much to see for free and great meals on offer that you might enjoy going there.

If you want to go into Dallas proper, rent a car on a day rate and carry your gear with you. You will need time to do all that.

I hope this helps. Welcome to Texas!