Air carrier pilot reported that while they were being vectored after going missed approach; they descended below their assigned altitude resulting in flight below the MVA. The flight crew verified that they were clear of terrain and landed safely.

Narrative

Descent below ZZZZ minimum vector altitude in the 7;000' sector north of the field; at or around 10-14 DMEWith the clouds broken at/around 6;000' and having been vectored off the STAR; on the previous RNP XX approach the controller kept us at 6K' and then cleared us for the approach at/around 10 DME. This made a stabilized approach impossible. We elected to go-around by deconfiguring the aircraft and accelerating. It sounded like the controller's supervisor took the radios and began directing the missed approach. We climbed back to 6;000' and turned downwind.On downwind the original controller came back on the radios and instructed us to fly 20 NM past the field and turn right and proceed direct to ZZZZZ for the RNP XX.We requested direct ZZZZZ1 and a descent to ZZZZZ1's crossing altitude of 5;500'. The controller approved the request and we began a descent. The controller then stated our descent must be in VMC conditions. We leveled off; checked our position and realized we were below MVA. We confirmed via EGPWS (Enhanced Ground Proximity Warning System) and FD (Flight Director) Pro moving map that we were clear of terrain; maintained altitude and continued the approach. We landed without incident. Cause: Inadequate controlling: On the first RNP XX approach; the controller struggled to provide adequate vectors and descents to enable a successful approach to a landing. This was evident when he cleared us for the approach at 6;000' 10 miles from the runway; and the controller's supervisor taking the radios.2) Loss of positional awareness while attempting to mitigate inadequate controlling and a clearance to self-navigate 20 nm north of the field while flying in and out of the broken clouds at 6;000': Intending to ensure a successful second approach; we requested direct to ZZZZZ1 and a descent to its crossing altitude. Additionally; the controller approved our descent and then moments later stated it must be in visual conditions.