GFI issue in bathroom -trips 3 recptaces - will not reset

The device does not need to be plugged into a GFCI receptacle. One GFCI receptacle equipped, like most, with a feed through feature. The one GFCI receptacle can protect several down stream receptacles.
Rig manufacturer will at times wire the whole rig on one GFCI receptacle to protect all standard receptacles.
Some appliances like the micro wave and refer (dedicated receptacle)are not required to be GFCI receptacles, but they are wired into one.