The movie was probably made in the 80's or 90's maybe

It is animated and starts with to two adults (kings or counselors, maybe) and a young prince and baby princess (who is not his sister) rowing away from a castle (possibly burning). Later the prince is shown as a teenager/young adult and is traveling with some gypsies and dances with a bear.

For some reason (I can't remember) he leaves and come across a shack and a young girl (the princess) and an old lady. He eats there, and they feed him goats milk. I remember it cause it was a funny scene because he drinks all the goats milk and the girl walks out to milk the goat again.

Later in the movie, for some reason there is a king who wants pigs painted (Botticelli style) all over his palace. His daughter is very pig like in looks and I think she tries to flirt with the prince.

Sounds like,.

The Treasure of Swamp Castle
a.k.a. Szaffi

view scenes
(I'll assume it's the original Hungarian)
I couldn't find the Eng. Dub.)

starts out with to two adults (kings or counselors, maybe) and a young prince and baby princess (who is not his sister) rowing away from a castle (possibly burning).

Later the prince is shown as a teenager/young adult and is traveling with some gypsies and dances with a bear.

he leaves and come across a shack and a young girl (the princess) and an old lady. He eats there, and they feed him goats milk.