Would it be weird if I invited myself over?

The mom of a friend to my 6 year old son asked that he come over swimming with them. They just put in a pool. The pool has a diving board, meaning there is a “deep end.” I saw pics of her son going off of it. My son can’t swim very well. I don’t know the mom at all. I’m nervous sending him there. I asked if she would be with them the whole time, and she said yes. But I’m sure she’ll need to run inside to go to the bathroom or something. This friend and his brother (around age 8 are very wild. I’m really nervous would happen if she leaves them alone just for a second. In my mind, I picture one of the boys saying, “Hey, let’s see how long you can hold your head underwater” or pushing him off the diving board. I’m considering telling her that since he can’t swim really well, I’m going to go with him. I asked my son if he would rather that I go or wear his life jacket. He said he’d rather me go. (He’s only 6, so he’s not embarrassed by me yet ). How rude is this (me inviting myself), and/or am I too paranoid?

It isn’t rude to invite yourself over. I never let my kids swim unless I was right there with them and they are older. I don’t even trust someone else to watch them so I would just ask if you can tag along or he can’t go. Swimming can be dangerous honestly.