Perhaps if you just make sure to eat and drink a bit more often on the bike (like if you normally eat every 45 min, eat at every 30 min instead) and go at a comfortable cruising speed during your first ride, you won't be too tired for the second the following weekend?
(I assume you've already covered bike fit, and found your preferred electrolyte replacement drink and carbo rich bike food.)
It might be a matter of pacing yourself and keeping fueled so you don't dip into your body's reserves, so you will not be so tired for the next weekend. If your 65 mile ride took 7-10 days to recover from, maybe going easily can cut your recovery time (and your body had done this before, so it might recover faster anyway.)
"If Americans want to live the American Dream, they should go to Denmark." - Richard Wilkinson