Cosmology - Why the Universe is Expanding at an Increasing Rate

Two Things: First, your video resolution is all wonky, I actually can't see all the video at the same time. Second, there are two things that affect time dilation, speed and acceleration. If you are "out in space between the galaxies" you are either traveling at a fairly high rate of speed, or would be by the time you go there, and you would still be under the gravitational influence of both galaxies. The factor you are looking for is called the "Lorentz Gamma" function, which describes time dilation as a difference in velocities. It's worth remembering, that time "is relative" rather, the passage of time will be relative between two different frames. Since everything is always moving, there is always a relative difference in the passage of time, given as delta-V in the lorentz equation. I would highly recommend Leonard Susskind's stanford lectures on classical mechanics and cosmology. They will likely answer more than a few of the questions you seem to be having.