Weird play - curious about rule

[box_elder]

Had the following play happen today and I'm curious about the official rule, though it's one I probably won't see again.

Young girls fastpitch. They were playing *without* infield fly rule, which caused the weirdness.

Bases loaded and either 0 or 1 outs. Batter hits a short infield fly towards third. All runners start advancing. Third baseman couldn't get to the fly in time and it dropped.

Runner from third returns to third base after ball hit the ground. Third baseman fields the ball and tags runner from third while runner is standing on third. Third baseman then touches third base.

Should it be a double play at third, since runner is forced to advance on the hit (no infield fly rule in play)?

Can the runner remain on the base "safe" from tag until third baseman either
1) throws home for the force
2) steps on third to force out runner from second and removing the force for runner at third
3) runner from second arrives and two players attempt to occupy the same base