Wishful is synonymous with hopeful or desirable in this case. The Tradition in this sense refers to the things your family members have spoken down from ancestors to descendents.
The version of history each parent taught their children that they were taught they were born of noble blood. They want the tradition to be true, perhaps either because being somehow related to the nobility is a source of pride for the family or because they receive some benefit from it. It is more likely the former option than the latter one, since the benefit would serve as circumstantial evidence of the history.
The primary implication is that since they are hoping it is true, they do not know actually know for certain if that is the case. This further indicates that the familial relations were made somehow ambiguous. Perhaps the family went separate ways or perhaps there are rumors of some sort of scandal. Some of the family might believe their alleged history is true and others might be skeptical of it but it's something that would be considered nice to most if not all of them.
Another possible implication is that the family does not voice any skepticism to the sentiment and perpetuate what might be fanciful lies to their children. This might be since it is more desirable than the alternative of just the known facts or perhaps more altruistically because they exhibit trust in their ancestors.
It's an odd use of the words by contemporary standards. I believe a major contributing factor to that is because in fantasy, wishes are often granted by agents like of Robin Williams and Barbra Eden or things like wishing wells and shooting stars. This predisposes us us to believe merely making the wish will realize it.
Another factor to consider is that many of us think of traditions much more narrowly than we did in the past, limiting them to the unique behaviors exhibited by multiple generations of our families, rather than the heirlooms or the things they've taught.
I think it's time to stop with the conjecture now though otherwise I'll just be rambling.
Referenced definitions are found in Noah Webster's 1828 American Dictionary of the English Language.