There is no format for a letter of explanation. And in fact, many marriage certificates do not even have the information for the bride or groom's parents.
The only part that I am confused with your post is that "your uncle stand for her". Does it mean she was not physically there during the marriage?
Proxy marriage is not recongized in Canada. If both you and her was there, then there is no problem. A witness can be anyone on a marriage certificate as long as it's recongize in the country of issue.
It is a letter, in which you explain something. That's it - that's the format. ))
I understood the post to mean that in the ceremony, the uncle stood in place of the father (in traditional ceremony).
To me all that needs to be explained here is: we are not in touch with father; applicant uses mother's name and not father's family name; father was not present at ceremony but other relative (uncle) topk the traditional roles; father's name was also not on marriage certificate.
Just state the facts, no need to go into long explanations. Lots of people come from households where they're not in touch with one parent / are estranged from various family members, etc. Absence of father's name in marriage certificate may or may not be a bit unusual / out of ordinary in local custom, but also not rare, nothing to worry about if just explained.