I bring 2 of my 4 dogs here and they love it. The area is large and correctly fenced with double gates. The hours are posted on the gates at both North and South Ends. The dog park is located at the South West corner of Shawnee Park. There is plenty of street parking along Mesquite or you can park in the main parking lot for Shawnee Park and walk west to the dog park.
For the most part the people who bring their dogs here are pretty respectful. I would like to point out that there are a few people who seem to be there a lot that really have no clue how to handle a dog, much less their own. The two dogs I bring are small, 12 lbs and 15 lbs. They are well behaved and well trained. If your dogs are well trained then you should not have any trouble. There's a large water station and various toys laying about for all the dogs. There is also an inner fenced area with agility obstacles placed throughout. If you have a small dog, they will love the inner area.
I would say go there and walk the property to check it out. I've found that the problems I had with other dog owners were squashed by simply going on a different day or time when they weren't there. It's a nice dog park attached to a nice park. Bring your dogs to your next BBQ and run them around the dog park to tire them out and then enjoy the many covered picnic tables and BBQ grills located between the dog park and the parking lot. There is also a large kids play area in the same vicinity.
Nice dog park, grass well kept, fenced inner area for smaller dogs. 4 Stars.