Can they touch each other? Hug? Are they allowed to expose their legs, arms, etc., in front of each other? Can they swim together? Dance together?
The Misnah Berurah in Hilchos Krias Shema says that the same hilchos Tznius applies for siblings as it does for other people.
If I recall correctly, Yichud is okay short-term, but not preferable long-term.
Here's the Rambam (Laws of Prohibitions on Relations Ch. 21), I don't know what the other opinions are.
So the first point here is that this is about grown-ups. For four-year-olds, well ask a child psychologist how much exposure is healthy, I guess.
So affectionate touching between adult siblings is not recommended. (Though I recall reading of a Baalat Teshuva who came from a non-observant, very-huggy family who was allowed to hug her brother at his wedding, as it's only "distasteful", not prohibited like hugging someone else's spouse.) Similarly Rabbi Moshe Feinstein wrote that if a rabbi sees people kissing other people's spouses (something downright prohibited), he should absolutely correct them. If he sees people kissing their grown siblings of opposite gender (or aunts/uncles), which is merely frowned-upon, it's the rabbi's call whether to say something.
As far as how clothed they need to be in front of one another (which is basically the question of mixed swimming), I'd think just applying common-sense boundaries would be appropriate. Not sure exactly where to draw those lines.
As for dancing, if dancing = hugging, then we'd apply the above Rambam (distasteful and strongly not recommended). If dancing is less than hugging, then I guess it's some common-sense boundary question. Rabbi Yehuda Herzl Henkin has some sources that according to some, social dancing was prohibited "as it might lead to affectionate touching", not that it itself was. (And of course there's dancing, and then there's dancing ...)