Mr. Engineer --
This is kind of grey area in Canada.
Each of us has the right to control commercial exploitation of our images. For those of us who aren't Sydney Crosby, the value of that commercial exploitation may not amount to much. However, there is currently no explicit protection for non-commercial use of our images in the common-law part of Canada (there is an older case from Quebec you can read about
here) -- though I suspect that may be coming some day, with all the new privacy legislation in this country.
So, your anonymous family does have the right to control the commercial exploitation of the image, which may include its use in a contest. I wouldn't say that submitting the photo is definitely off-limits though. I think that if it came to it (and I can't actually believe it would -- if the family got wind and objected, you would just graciously withdraw the entry) and the thing went to court, the court would look at all the circumstances of the contest before deciding whether submission constituted commercial exploitation.
The other thing to consider though is whether your contest has rules about submission of images of people (which it really should). I would think that any serious contest would require entrants to certify that they have obtained releases from any persons who are the main focus of their photographs. If you submit your photo, give the certification, the family hears about it and it turns out that you don't have the requisite release, well, that could be awkward and embarrassing.
EL