Not much one can do about the misdeeds of their family, justtry. The fact that you have good references is a plus. Now, as to your polygraph:
Please remember that truthful people get judged as liars by the ploy, er, poly. You might well pass doing nothing but telling the truth, relaxing, and playing "Sailing" by Christopher Cross in your head
Or, you might run into a particularly noxious couple of relevant questions, be honest on the controls, and end up with spiked readings on the RQ's versus flat readouts on the controls. That is messageboard-speak for you fail, go find another job.
(The way to insure passing is to make your control questions, or CQ's, visibly more indicative of a reaction than the relevant (important) ones, or RQ's).
You would want:
(control) Have you ever lied to get out of trouble? to cause an increase in physiological responses, while
(relevant) Have you ever committed trainbombing? to show no reaction, or at least less of a reaction.
I use trainbombing because it would be introduced to provoke a visceral reaction by its innate repugnance, your own surprise, or the fact that you have to assimilate a word you don't hear often. If you get a question sounding something like that, I suggest you might have a particularly poor (or malevolent) polyboy, of which there are plenty. They're not supposed to go into sex, politics, religion, trade unions, or racial opinions; nor are they to use words that by themselves tend to evoke a large reaction. However, these "rules", which are really guidelines, are sometimes set aside for whatever reason.
If you get something like this, stay cool and go with the flow. More likely, you'll get
(treat as relevant) Have you ever committed a felony? That's general enough and not anxiety-provoking.
Good luck to you...