as a matter of fact, the acceleration is only 2g but since accelerometer only measures force, it reports 3g
That depends whether you are working in an inertial reference frame.... 3D accelerometers are neat precisely because they understand F=ma and general relativity! They only read zero in free-fall.
Which part depends on inertial frame? 2g acceleration or 3mg force measured by the accelerometer?
Why is general relativity mentioned here?
According to general relativity there is no difference between acceleration due to gravity and any other kind... No experiment can distinguish them. In particular an accelerometer can't so it sees an acceleration of 3g at the bottom of the swing caused by the tension of 3mg in the string.