Sorry in advance for the wordy reply; I tend to get very precise with my explanations...
I can't really answer the first question as I have a different rig, but will tell you I have had great results with Winegard Pathway X1, which is exclusively for Dish Network. They have a comparable model, the Carryout G2 (Winegard Carryout G2 - HD Portable Satellite TV Antenna
) which works with Direct TV or Dish. My X1 is powered by the receiver so there is no need for a separate power cable, a big plus for me; the G2 does have a separate power cable. Both of these units can be used free-standing (ground, table, tri-pod, etc) or mounted to the roof with a mount kit that is like $50 (Roof Mount Conversion Kit for Winegard Portable Satellite TV Antennas
). Both support 2 receivers; mine came with 1 25' coax so you'd have to supply your own for the other.
I plan on cheating a bit
and hooking up to the dish and cable in some campgrounds, partly to avoid losing some channels on the secondary receiver (it is somewhat dependent on which satellite the primary is tuned to; don't know if Direct TV works that way, but Dish has 3 satellites tto choose between) and also to provide cable feed to my outside TV coax as I haven't bothered trying to reconfigure wires to send Sat signal out there. Plus the cable won't go haywire during heavy rains. I did it last trip and worked to perfection!
One advantage of not mounting to roof (I haven't done mine that way yet, and may not) is that is you are in a shady area and view of south sky is blocked by trees at least from the roof, you can move the unit to an area that is not blocked and get a signal. I had to move mine off to the side of the rig on my last trip, and once I did things worked great!
Below is a link to site to view their other options; I bought mine on sale from Camping World and got a $50 gift card in mail to boot!
Portable Satellite Dish - Winegard Portable Satellite Antennas, Mobile DIRECTV, Mobile DISH Network
I wish you luck in your search.