Typical dome installation has two coax feeds, one to the bedroom and the other to the entertainment center. Yes two feeds.
But the dome does only have one LNBF which means only one satellite at a time. You can watch two different channels as long as they are on the same satellite.
What you can't do is use a separator to feed both VIP222K inputs with one coax from the dome. You have to get both dome coaxes to the same place.
Depending on the age of the dome, it may needs a firmware upgrade. Before you spend too much on the dome, consider a Winegard Trav'ler replacement.