"Kvankam" comes from the Latin "quanquam", meaning "although".
So much of the Esperanto vocabulary is derived from Latin.
This would have been a great time to introduce tamen. It's easier to think of kvankam and tamen as a pair.
"Kvankam la vetero estas malbona, tamen la infanoj ludas ekster la domo."
It's true that they have similar meanings, but using both together is superfluous and sounds clumsy. One or the other alone communicates the meaning.
Awkward. Although the weather is bad, however, the kids are playing outside. It only sounds right when trying to emphasise something.
Would it be grammatically correct to say just "la infanoj ludas ekster"?
Other than "ekster" changing to "ekstere", your sentence is fine.
Thanks for your help!