It would seem the difficult citation against raising a Charter of Rights claim is Lee v Canada (126 FTR 229) in which the court said:
The applicants have no standing to bring an application for a Charter declaration in their capacity as TEPA’s henchpersons. The Charterdoes not apply extraterritorially in order to allow TEPA to make an effort to break through the frontiers of Canada, and counsel’s suggestion that it could mount a horde of declaration applications is not well taken. Conformity with Canadian law is all they need, nothing more nor less.
The members of TEPA who dislike the policy of heightened scrutiny have no standing to invoke the Charter: Madam Justice Wilson in Singh et al. v. M.E.I.,  1 S.C.R. 177 at pp. 201-02; as to lack of standing – Canadian Council of Churches v. Canada,  2 F.C. 534, at p. 563, where the Canadian Bill or Rights was also invoked in an immigration matter. Those who are non-citizens, outside of the territory of Canada cannot invoke the Charter as is purported to be done here. Also illustrative of this proposition is Ruparel v. M.E.I. and Secretary of State,  3 F.C. 615.
This seems like a rather strident position to take (that only citizens within Canada have Charter rights that can be invoked) but it may also reflect the annoyance the Judge held for the Applicant in this case (they’d already been awarded resident immigrant visas yet were in court trying to argue about the way in which it was done.) It does suggest a couple of things to me, however: first, that my spouse might have rights to intercede (“standing”) in this case and assert Charter rights (being a citizen within Canada) and that I might have rights because I’m within the territory of Canada, although not a Citizen of Canada. The cited case is old enough I couldn’t find it online (not yet, at least.) I’m sure I’d find it if I wandered down to the law library (I’m only two blocks away from the courts here in Vancouver.)
I did find some interesting analysis of this issue from searching for this citation. For example, this piece “Independent Immigrant Selection Criteria and Equality Rights : Discretion, Discrimination and Due Process” was insightful, albeit older and thus lacking in coverage of more recent applicable case-law.
My thinking right now is that if Lee v Canada can be overcome in this case, the remaining part of the argument is actually quite straight-forward (the Auditor General report and CIC’s admissions are very solid bedrock upon which to build a case for known discriminatory conduct.) Then arguing about the reasonableness of the restriction is certainly the fun part.