Oklahoma is a landlocked state so no 'beach.' However, there are many lakes in the area but none have houses for rent on them. If you're fine with a hotel, I'd recommend Hampton Inn in Bricktown. They have an indoor pool that I've seen lots of kids in and there's a lot of walkable activities in the area including Hey Day and Brickopolis that have laser tag, mini golf, bowling, etc. Also the Riversport area is quite fun for a day activity with the kids.
Do you want to be in OKC or are you willing to consider visiting some of the lakes in OK? As mentioned there are several lakes in OK and some do have vacation rental property on or close to a beach/dock area. Take a look at VRBO.com for Grand Lake O' the Cherokees, Tenkiller, Eufuala Lake, etc. You can look on a map and see lakes in Oklahoma and then search on VRBO or a similar site. Some of the lakes in OK won't have rental property with direct beach access because the Corp of Engineers owns (maintains, I'm not sure the legal status) the shore front land.
As mentioned above, Bricktown and all those activities are great if you prefer to be "in" OKC.
I wasn't thinking that 4 hours from OKC was near but I also didn't think about they were already traveling so 'near' is relative :-).
There are MANY fab lakes that will likely be airbnb/VRBO and even cabin rentals (although not sure Broken Bow has them). Lake Murray, Texhoma, Tinkiller, Greenleaf to name a few not mentioned above. None of these are within an hour of OKC though...