As many have said, go during the week. No lines to speak of.
Many rides have minimum height restrictions, so a 3 yr old may be too short for all of the rides. Lots of rides for the kids and adults. All are 'mild' if you're comparing it to Six Flags, but enjoyable nonetheless. To access from the train station (arrived from Kyoto) - walk straight ahead, take the first right and its directly in front of you, about a 60 yd walk. Easy.
I'd avoid the 'snack shop' across the Mouse / Log ride. Nothing good there. They have better food at the street down by the kiddie rides (go right from the entrance area). McDonalds and other choices.
Purchase the Keihan Sightseeing Pass for Hirakata Park - all day rides on their railway + admission for 1,000Y (vs 1400Y). Also discount on the 'all access' pass (2700Y vs 3000Y). You can only exchange prepurchased vouchers at the Keihan Stations. To purchase the pass in Kyoto, you need to go to Kyoto Station, where its sold in about 4 places, but all in the same small area.