Assuming all this childish bickering hasn't put you completely off coming to town at all, let me just say you can find fun or interesting things to do in most areas of Dallas...they all have their merits and their negatives, your best bet is to pick specific things you want to do rather then just driving aimlessly into neighborhoods.

Fair Park has always been just fine during the day. I can't imagine what there is to see in Denton..spent a year in college there, and there just isn't much in the way of "sights". Granbury is cute...I wonder if they still have the drive in movie theater? Might be a kick for your child. :) It's a bit out of the way, but you could make a trip into Ft. Worth, then to Granbury and stay the night there (with a side trip to the park near Glen Rose...name fails me but it's known for it's dinosaur tracks). Ft. Worth zoo is better then Dallas. Hillsboro only has the outlet malls, but Allen (just north of DAllas/Plano) has an outlet mall as well, and is much closer. East on LBJ won't take you anywhere but around run down, warehousy area (Garland)...unless you drive much farther out, and the only thing out there is the Mesquite Rodeo. White Rock is nice enough for a picnic, room for your child to play, just don't let your child go alone into the restroom.

One cute thing for you to do, entertaining for a "family" type thing, is there used to be the Tarantula Train (old fashioned train) running from Grapevine into the Stockyards. You get to spend some time touring around the Stockyards, and the they bring you back.

Good luck, I hope you have a great time :)