My family and I are going to St Louis in June and thought we'd stop somewhere in Kentucky to break the trip up. We're traveling from Alabama. We have a 2 year old and a 6 year old, both girls. Any tips on what they might like to see for 3 or 4 hours between the TN/KY state line and Paducah? Any small beaches on Lake Barkley or Kentucky Lake? This area looked interesting. We wouldn't mind driving a couple hours out of the way to see something interesting. Tips on where to stay 1 night?

There is a small beach at the northern end of KY Lake, exit 27 I think, just follow signs to KY Dam. Exit 31 leads to the Land Between the Lakes area, if you drive south from the interstate a few miles you will see signs to Patti's 1880's settlement (http://www.pattis-settlement.com/home/). They have some kid-friendly things, animals, a waterwheel, miniature golf. Best hotels are in Paducah at exit 4, several with an indoor pool. Downtown Paducah is nice. If you are there on a saturday night they have "Downtown after Dinner" which is live music among other things (very family friendly). I would recommend staying in Paducah, although there are a few hotels by the interstate in the lakes area. The first exit in Illinois (Metropolis) has a recreated French and Indian Fort (Fort Massac)which kids love.
I live in Paducah and will be glad to answer any specific questions you have.

If you are traveling on I65 be sure to stop at Mammoth Cave and take one of the short tours. Everyone will need a jacket and maybe some kind slacks/pants to wear while in the cave as it can be chilly. http://www.nps.gov/maca/home.htm

Bob, does Dippin Dots ever give Paducah tours?

Bob, is all of KY Lake area still dry (no alcohol)?

I'm not sure on Dippin Dots, their phone # is 270-538-0502 or 270-443-8994, if you want to call them.
I am pretty sure that the counties right around the lakes are dry, McCracken County, which is about 10 miles east, is not dry.