If force is what causes gravity (motion), what is causing force?

Why do you think "force is what causes gravity" in the first place? In General Relativity, gravity is not a "force", so your whole OP is based on an incorrect premise.

 

No, you are missing language: the language of relativistic invariants. All of these "words" that you say "aren't cutting it" are *not* the words that GR actually uses to describe the underlying physics; they are words that people overlay on the underlying physics to try to make it match up with their intuitions.

The language you should be using, if you want to describe the underlying physics the way GR does, is the language of covariant and invariant quantities: things like the metric tensor, the curvature tensor, proper time (as opposed to just "time" without qualification, which is ambiguous), etc. So the real problem is not that the words of physics don't cut it; the problem is that you are not using the words of physics, you're using the words of lay people's intuitive picture of physics.

 

It depends on what you mean by "force". That's why "force" is one of those words that doesn't appear in the underlying physics, but only in lay people's intuitive picture of physics; it's ambiguous and doesn't really match up well with the underlying physics.

According to GR, "gravity" is a manifestation of spacetime curvature (some physicists would say that gravity, or at least tidal gravity, *is* spacetime curvature; they are just two different words for the same thing). That makes it fundamentally different from things like electromagnetism which are often viewed as "forces": an object moving solely under the influence of "gravity" feels no weight and has zero proper acceleration. Objects moving under the influence of other "forces" do feel weight and have nonzero proper acceleration.

According to quantum field theory, "gravity" is a manifestation of a quantum field: a massless, spin-two field, to be exact. Other things that are often viewed as "forces" are manifestations of other quantum fields; electromagnetism is a manifestation of a massless spin-one field, for example. On this view, "forces" are just particular manifestations of quantum fields; but not all such manifestations are usefully viewed as "forces". "Gravity" is just another quantum field on this view, but it still does have some unique features--the ones that lead, in the classical limit, to the GR view of "gravity" as spacetime curvature rather than as a "force".

 

"Motion" wouldn't work any better, since it's also relative. In SR and GR, you don't actually need the concept of "motion" at all; you can analyze everything using spacetime as a 4-dimensional geometric object, with the worldlines of objects being curves within this geometry, and all of the physics being contained in geometric quantities like the lengths of curves, the angles between them at intersections, etc. (Similarly, in quantum field theory, you don't need the concept of "motion" either: you can analyze everything using path integrals, which is basically the quantum version of the "spacetime" viewpoint in SR and GR.)