How many days are you planning to stay? I think the coast of the Bay of Kotor is a little warmer than the Adriatic Sea in early June. I once read an article about the history of Montenegro that mentioned some interesting facts about its geographical location and weather conditions. I recently came across an article on getexperience.com https://getexperience.com/blog/posts/best-time-to-visit-montenegro about how things are there now. It gave advice on when to go on vacation. I think you’ll find it useful. Based on my experience, I can assure you that children will definitely be able to swim there in early June.