What would you do?

[WC Nightmare]

Runner on 2nd and 3rd, Batter hits fly ball to right field, Runner on second takes off and runs into the shortstop (obvious obstruction), the ball is caught and thrown to second for the force out.

Do you send the runner back to second or call her out?

[WC Nightmare]

No she ran into her coming off of 2nd.

[Comp]

Rules supplement 36 states that the runner cannot be called out between the bases when obstruction is called does not apply when the base runner has committed another violation and that violation is being played upon. It uses an example very similar to the OP, however, in the example the runner is obstructed while trying to return to 2nd, but would have been thrown out regardless of the obstruction. In this case the runner would still be ruled out.

You are now into a pure judgement call by the umpire. Did the obstruction that occured prevent the runner from returning to touch 2nd base prior to the live ball appeal?

[MTR]

Runner on 2nd and 3rd, Batter hits fly ball to right field, Runner on second takes off and runs into the shortstop (obvious obstruction), the ball is caught and thrown to second for the force out.

Do you send the runner back to second or call her out?

A, It is not a force out. It is not possible to have a force out on a caught fly ball.

B. How was the runner obstructed? Was the runner impeded advancing to the base needed to obtain to be safe?