Hi Jenny,
I work in Lexington, Kentucky and have general knowledge of the area. Granted I do not have kids, so most of the activities I are enjoy are not kid-friendly. With that said, i'll try to identify activities that might be of interest.
*Kentucky Horse Park and Old Friends Thoroughbred Retirement Home (as mentioned by conniejj). There's also Legacy Trail which is a 8-9 mile biking/walking trail.
*Keeneland - the spring meet starts April 5th. I recommend a week day visit (weekends are insane).
*Horse Farms - there are countless horse farms in and around Lexington that you can tour (i'd call and schedule in advance).
*Bourbon Trail - yes, I am aware this is likely not kid-friendly. However, I find the history behind the bourbon distilleries fascinating and most of the distilleries are located in horse country (i.e. beautiful scenery).
*Children Explorium of Lexington
*Cincinnati Children's Museum - located a little over an hour from Lexington, but well worth the time. My nephews (ages 6 and 2.5) love the museum!
*Raven Run Nature Sanctuary - hiking trails and outdoor stuff (never been there myself, but have heard nice things)
*Gatti Town (pizza, video games), Bounce U and Monkey Joe's (blow up bouncy things), and Champs Entertainment (indoor roller skating ring, laser tag, miniature golf, etc.) - These are not unique to Lexington, but still fun activities for kids.
*Mary Todd Lincoln House, the Hunt-Morgan House, the Henry Clay Estate - I fear your children may not find these interesting, but if you/they enjoy history, they are worth a visit.
*Lexington Children's Theatre (not such what's playing right now).
*The Arboretum - the state botanical garden. If the weather's nice, it's a relaxing, fun place to visit and explore.
*Shaker Village
If you have any questions, please feel free to message me.
I hope you enjoy Lexington!!