grammar - "... due to their not being citizens ." - is that a reasonable use of "their"

I wrote a sentence just now and after I'd pressed 'send' I began to wonder whether what I had written was correct.

The sentence read

They were ineligible due to their not being citizens

An alternative - it seems to me - could be

They were ineligible due to them not being citizens

but that sounds a little clunky.

Is there anything wrong withe the first one ?