I personally would
never put my neighbor in a position of legal liability for the use of their constructed or purchased floating dock.
I was brought up to stay out of other people's property unless invited in. This included cutting through neighbor's yard whose kids I played with, but were not playing there at the time. Our kids were brought up the same.
Yeah, I know, public lake, public water, but hopefully if you moor a boat on your small, basically unregulated lake, no one will climb on board and take it for a spin
.
IMHO, if you want the kids to have a swim platform, buy one or make one. In the meantime, use your beach. Again, just my opinion.