Many Beech Sierras and some Musketeers/Sundowners were built with a
child seat in the baggage area, and were certificated to carry six
people. I own a C24R Sierra (with 4 seats) and have also flown an A24R
with pax in the "way back", as my son used to call it.

The Sierra generally has about 1000 lbs useful, minus 60 gallons of fuel
leaves 640 lbs payload---plenty for two adults and three small kids. If
you stick with two 150lb adults, that leaves 340lbs for kids, dogs, and
bags, and that's only if you insist on full tanks. I should note that
the Sundowner gross is a bit less, but still plenty for your stated mission.

Additionally, these models have a huge baggage door to enable access to
the back, and the Sundowners and Sierras have a pilot's side door as
well as passenger side.

Economically? Yes, very. I get better mileage than most SUVs---my C24
cruises at 135 knots on 10.5gph, but if I throttle back just a little I
can get 131 knots on 9.5gph, close to 14nm/gal. Price-wise you can
probably locate a decent Musketeer Super III (model B23) or Sundowner
(C23) for under US$45k, or a Sierra for US$55-70k.

Fast? Not for a retract, but it's not a race. With a seat that comfy
and a view that nice, I am in no hurry. The fixed-gear Musketeers are
quite a bit slower than that, BTW, but the same logic applies.

Note that many Sierras were built with only 4 seats, and installing the
back seat retroactively is a very difficult thing.

Here is a good place to visit:

http://www.beechaeroclub.org

hope this helps