When we measure really distant red shifts...?

George is correct about the peculiar velocity (the velocity of an object not associated with cosmological expansion). At far distances from us (z>1) it is often so much smaller than the recessional velocity due to cosmological expansion that it is negligible. It can play a big role in observing clusters of galaxies nearby though. The rotation of the galaxies around their cluster center can provide a peculiar velocity that is comparable to the recessional velocity. To this effect, you can easily distinguish the two by calculating the theoretical radial velocity from Hubble's law.

Conveniently, v=Hd applies quite well within our local region of the universe so that you can use that simplified version of Hubble's law to get the radial velocity. Then simply subtract that from a measured velocity to get the peculiar velocity. At far distances where v=Hd doesn't apply, the peculiar velocity is so small that it wouldn't even be measurable anyway due to the large experimental errors in measuring distance.

The motion (ie "peculiar" motion) of very distant galaxies is extremely small relative to the cosmological expansion rate. [This is based on the cosmological principle that says what is way out there isn't highly abnormal to what we would expect.]

[It is not commonly held that Doppler motion is the correct explanation for the redshift of distant galaxies. They call it something else, like the "cosmological redshift". I like the Doppler idea myself, but I'm no cosmologist.]

At large redshifts, proper motion isn't important. For example, you can measure the movement of Andromeda (approaching us at 300 kilometers per second). Recession speeds of that magnitude are achievable by galaxies 3 Megaparsec away.

From what i gather from my own knowledge and reading the other responses it seems like the universe is expanding at a higher rate as we look farther. Its almost like the universe is being sucked into a vacuum but were not as close to that vacuum as some of those distant galaxies.

We will know it when it does not matter.