I'd say it can very seldom mean "is this the mother?", because it means that the speaker talks of a definite person who is neither his nor his addressee's mother (otherwise "the" would not have been used), and here Slavic languages use longer constructions, like "Is this the same/the very mother?".
Yes, it has a very specific contest but it is a valid translation. For instance, a doctor expecting to examine a (future) mother receives a woman in his office, checks his name list, points to her and asks: "Is this the mother?". In this case you definitely translate it as "Це мати?" to Ukrainian. So --> totally valid, should be accepted
It can both mean "Is this Mother?" and "Is this a/the mother?" depending on the context. If you had to specify, you would use sentences like "Is this our mother?" or "Is she a mother?" or "Is this the mother we talked about earlier?" You should understand, this is only a basics lesson where you are taught simple sentences. Most of them rely on context.
I'm still in doubt whether to accept "that" as a translation of "це". On one hand, це = this and то = that. On the other hand, the meanings of "That's mom" and "This is mom" are very close and the phrases are used in the same situations.
Another point is that, going through different exercises I see that in some "that" is accepted as a translation and is some it's not. Apart from being correct or wrong, it has to be consistent... If it's one way in one exercise, it should be the same way in another one...
I don't know if I can decided these things by myself or should consult with other moderators and administrators. I probably should, but I've been bombarding them with really a lot questions these days already :'D
More often "це" is "this" or "it" and "mom" is "мама".
Other words are used for that perhaps more often: http://www.freelang.net/online/ukrainian.php?lg=gb http://www.cybermova.com/cgi-bin/olenuapro.pl