I think the fact that your father won't respect your wishes with regard to your own children must make things very difficult for you.
He says that he wants to look after them, which is great, but he needs to acknowledge that, as their mother, your beliefs about whether something is appropriate for these children are paramount to his views.
I feel for you, OP, because the main issue here should be your feelings, not your father's.
So what if it's no big deal to him that your children are naked in public - it IS a big deal to you, so he should do as you ask.
It must feel like you're trying to assert your authority, but being ignored, which would be very upsetting.
I'd want to know that the people caring for my children would do so according to the guidelines I ask them to follow.
I think I'd go for the nursery option, to be honest.
This isn't really an issue about swimming costumes and fountains, it's about respect, authority and control, imo.