I can't help with the Cincinnati side of things, but I do live about 10 miles due north of Cherry Hill park. The standard Google directions bring you I-70 then down 270 to 495. I wouldn't do this if you paid me to.
Instead, if you're not adverse to tolls (which you'll have already paid a crap ton driving out the OH/PA turnpikes if you take them), you can do I-70 then down I-270 to Rt. 200 to I-95 (link to google maps
If you want to avoid this section for tolls, you can do I-70 to Rt. 32 to I-95 (link to google maps
The holiday weekend is going to be heavily traveled. Some schools in this area are on Spring Break that first weekend in April. Driving Mondays and Tuesdays in the DC area are the best for driving. People telecommute and it only gets worse the later in the week you get. If at all possible, try to hit the DC area mid-day from 10am-3pm; after 3pm until 6-7pm is going to be much more busy.
Coming out of Cincinnati - Google offers some unique routes. The first option is the OH/PA turnpike. The other option seems to be some Rt. 32 to Rt 50. The second one looks neat, but I don't know the area at all.