correct words

Re: correct words
You can use either word in the highlighted pairs, as you prefer, but since it struck you (past tense), you should use "could use" rather than "can use".

I'm no native speaker, but I'd cut the sentence in two in order too remove some redundant words. Like so:

Then it struck me. I could use the family tree to trace who those strangers in/at my grandparents' house were.

Than again that wasn't your question.