"Your sisters are washing their hands."
Translation:Eure Schwestern waschen ihre Hände.
It isn't “ihren” because accusative plural of possessive pronouns ends in
-e, not -en and it isn't “Handen” because there's no regularity in plural formation (there is a limited number of ways to form the plural but you can't predict which one any given word is going to use) and you will just have to remember that the plural of “Hand” is “Hände”.
I'm not a native English speaker, but the way I see it, the English sentence is the standard phrasing you'd use to express that the sisters are washing their own hands, so that's what I read into it.
The standard phrasing in German, however, is "sie waschen sich die Hände", not "sie waschen ihre Hände", which sounds a bit like an anglicism (if that's the right word) - although it doesn't sound unusual anymore if you add e.g. "Sie waschen ihre Hände mit Seife" ("...with soap"), and for the idiom "Sie waschen ihre Hände in Unschuld" ("...in innocence") it's even the standard phrasing.
Shouldn't it rather be "sig"? I have no idea of Swedish, but it seems fairly similar to Danish, where sin/sit/sine are kind of reflexive possessive pronouns, that don't exist in this way in German, while sich is a reflexive (object) pronoun (3rd person sg. & pl.). It's rather like himself/herself/themselves, but used much more often.
Yes, exactly what I thought. In German that would be "Er mag seine Kinder", but we can't certainly know if they are his own children (sina/sine) or the children of sb. else (hans/hans). Even worse for the female version: "Sie mag ihre Kinder", where "ihre" can refer to her own (sina/sine), those of another woman (hennes/hendes) or another group of people (deras/deres). All of them would be "ihre". If you admit even "Ihre" (only a written difference), it would be "your children" (formally speaking). That's why I say German is lacking "sin/sit/sine"-style pronouns. I just came across them in learning Danish....