This is a Polish language teaching course so I may be a bit picky here. I know that just taking a sentence out if context is difficult, and we do not know what the preceeding sentence might have said, but this translation sounds a bit clumbsy . I think an English speaker would be more likely to say 'My mother and her are sisters'
'My mother and her are...' is not grammatically correct. You wouldn't say 'Her and me are going shopping', it would have to be 'She and I...' because they're the subject of the verb, and it's the same in this exercise.
Colloquially using object forms in a double subject is quite common, but never in a formal style.
It sounds weird to me, too. I would most definitely say "My mother and her". It may not be grammatically correct, but most native English speakers I know would say this, too. It just sounds more natural :/
Yeah, it would be nice to have context sometimes. Maybe a prompt similar to a word problem in math would be useful?
Her mother and my mother are sisters. How would this best be said? My mother and her's are sisters? moj matka i jej sa siostrami? Or would you have to use matka twice?