I used the VRE extensively before the pandemic and have taken advantage of the "Free Friday" promotion a couple time to take my family to DC on a Friday. It's a fantastic way to spend a day in the City. I'd love to see Saturday trains in the mix. Though, I do worry that the cost would be prohibitive. For example, taking a family of 4 up to DC from Fredericksburg would be between $48 and $73, with a need to jump through several hoops to get Youth Fares. The site does state "Children 10 and under ride for free with a fare paying adult." Though, they don't make clear what sort of documentation is needed to verify that.
So, at best, two paying adults and two kids under 10 is still $48.60 for a day pass. It's $72.90 if the children are both 11 years or older. Assuming $20 to park for the day (worst case), and at ~60 miles each way, gas works out around:
120 miles / 30 mpg * $3.50/gal = $14
So, right around $40-$45 when considering wear and tear on the vehicle. So, just about a wash for the family with two younger kids and pretty bad for the family with older kids. Also, there is the issue of control over scheduling and not having to carry everything with you everywhere in the city.
I really would love to see the VRE expanded and it's a great way to get cars off the road. And I think the Free Friday has shown that there really is pent up demand for it's use. But, increasing fares is going to keep a downward pressure on ridership.