Since it's pointless to look through all these pages I'll tell you what his "proof" is.
That she wanted to go on a vacation without him.
He went through her e-mails and she was corresponding with an ex (which she had told him about prior to him going through her e-mails).
She went on her vacation and he wrote down what her odometer was at, and he was going to look at it and calculate how much she drove when she comes back from her vacation to see if he's cheating on her. I'm guessing he assumes she'd go to where she's going on vacation and just not drive anywhere but from their place to the location and back.