Last summer we wanted to plan a trip our young boys would enjoy since they tolerated going to the South Arm of Knife for the previous 4 years. We did just as you are looking to do and headed to Insula to find a place where they could swim and lounge on the beach. The stars aligned and we ended up staying on Williamson Island and took a trip to a different beach every day. There are several to choose from and I would venture to guess you'll be able to find at least one empty one.
This is the site previously mentioned south east of Williamson Island. It's just to the right as you enter the north section of the lake.
Have a great trip with the kids! I will cherish the time I spend with my kids up there forever.