Not only is this not seen as alienating (although it often results in the undocumented parent being deported and never seeing her children again), but it is often recast as reprehensible conduct by alien mothers sufficient to
constitute immigration fraud and be grounds for an annulment of the marriage.
It seems that she may have been working without authorization, a violation of
immigration law (in Canada and the US), which would
constitute «visa
fraud» (in Canada, «misrepresentation») and lead to an investigation.