I had an interesting look at this sort of "relative" thing today, while doing a bit of orbitology. Specifically, I was playing around with differences between a couple of satellite trajectories. The normal approach is to look at the differences as a function of time, and I saw pretty much what I expected -- an oscillation in the position differences that grew with time.
However, I also had reason to believe that the three position differences had a "phase" relationship -- and so I plotted the component differences against each other. Along-track vs. radial differences formed a rather interesting spiral, as did along-track vs. crosstrack position differences. Radial vs. cross-track was obviously a tilted "side view" of a yet another spiral. What I saw as oscillations in the "position vs. time" plots was nothing more than a cross-sectional slice of a motion for which there was more than simply a time-dependence in the motion -- the actual motion was more complex than the position vs. time plots could show.
The point here is that your "relative to space/time" statements are very much like this -- perhaps what we see in 4D is likewise a cross-sectional "slice" of motion within a larger-dimensioned universe?
This is not of necessity, as I understand it, but rather because the belief is we ought to "notice" a higher dimension. That has always bothered me since our vision and minds are restricted to what appears to be four (seemingly arbitrary) dimensions out of n.
There's also the Randall theory that gravity is so small compared to the other fields because it is interdimensional. Branification: An alternative to compactification.
As you can see, there are theories for higher dimensional dynamics, as you suggest - and they are state-of-the-art. Below is one group I've been watching for quite a long time because they have doggedly avoided the compactification model. You might find their work interesting also:
Welcome to the homepage of the 5D Space-Time-Matter consortium. We are a group of physicists and astronomers working on a five-dimensional version of general relativity. Our work differs from Kaluza-Klein theory (the basis of superstrings) in that we do not assume compactification of the extra dimension. This means that new terms (those involving the 5th coordinate) enter into physics, even at low energies. In 4D spacetime these can be interpreted as matter and energy. We move them to the right-hand side of the 4D field equations and take them to describe an induced energy-momentum tensor. In fact, we have shown that no 5D energy-momentum tensor is required. 4D matter of all kinds can arise as a manifestation of a higher-dimensional vacuum. This is one way to realize Einstein's dream of transmuting the "base wood" of matter into the "pure marble" of geometry -- that is, of unifying the gravitational field, not just with other fields but with its source.