Translation:Her cat dances better than your dog.
"बेहतर" is not an English loanword. It is Persian, and as such it can be considered a natural part of the lexicon that made up the Hindustani language from its inception as a modern language born of Indic grammar and lots of Persio-Arabic vocab.
To answer more directly though, I personally feel that your construction is more natural or idiomatic (and I've expressed this on another example)... though evidently that is a matter of perspective since the creators of the course didn't think so. My point would be that your construction is not more correct per se but rather more common. Interested to hear what others think.
"se" is a postposition which puts "kutta" into its oblique case form, "kutte." Hence, the "kutte" you're seeing is the oblique case of "kutta" which means 'dog', singular. You're probably seeing "kutte" and mistaking that for the plural form of "kutta."
If "dogs" was intended, we would see the oblique-plural form, "kuttoṁ [se]".