Hi Al -
Time is relative, but the speed of light is not. One of the tenets that got Einstein thinking in the first place was the observation - not the theory, but the real data - that the speed of light is constant, regardless of the motion of the source or the observer (within inertial reference frames). What this means is that if you travel away from the sun at 99% of the speed of light, the light from the sun will still pass you at the speed of light - relative to you. And if a galaxy is receding from us at 99% of the speed of light, the light from that galaxy will still pass us at exactly the speed of light - relative to us (in fact, this is nearly the case with some recent observations of very distant galaxies).
This is not terribly intuitive, but it is absolutely accurate. No matter how fast you move away from (or toward) the sun, the light from the sun will still pass you at the speed of light. You cannot catch those photons. In fact, in a way, you are no closer to the speed of light when you are moving that fast than when you are standing "still" on the earth's surface.
The net effect of this is that, since the speed of light does not change with moving reference frames, other things like time, length, and mass must change as viewed from one frame to another. A simple equation like distance = rate x time changes dramatically when the rate is fixed.
As far as we know today, this is the way the universe works.
ADDED: OK, think of it this way. You are standing on an asteroid in empty space. A star ship passes by , and that ship is built entirely of transparent material, with mirrored floors. As it passes at near light speed, the pilot shines a flashlight straight down toward the floor. In his frame of reference, the light from the beam travels straight down and bounces straight back up, like this "|". But as you see him pass, the beam, in your frame of reference, travels down and then back up at an angle, because of the relative speed of his frame compared to yours. To you, the photons travel in a path that looks like a "V". The distance that he measures for the light path is shorter than the distance that you measuer for the same light path. You are both right.
The strange part occurs when you measure the speed. He sees the beam traveling at the speed of light relative to him. You also see the beam traveling at the speed of light relative to you. That doesn't seem like it could be right in our every day world, but it is the way that light works. Now, since the distance the light travels changes, but the speed remains the same, you can then see that the equation "distance = rate x time" is affected in a way that is not normal in our Newtonian experience. That is, if the distance changes and the rate remains constant, then the time must change. And that is indeed what occurs. The time to see the event of the light shining to the floor and bouncing back up again is different in your frame of reference than it is for the pilot. Neither is wrong. They are just different.
If you are saying that the speed of light cannot be constant, I'm afraid you will have to take that up with all the folks who have been measuring it for the last century or so. All light travels at exactly the same speed, whether we are moving toward or away from the source. Light from distant galaxies that are receding at 90% of the speed of light still arrives here at the speed of light relative to us.