Air Carrier Pilot reported while taxiing for departure another aircraft did not yield to their aircraft resulting in the crew taking evasive action to avoid a collision.

Narrative

The flight; Aircraft X; was cleared to push from Gate and on to taxiway 1 facing west.After push ground control cleared the flight to do a right turn at Taxiway 2 on to taxiway 3 hold short XX L. Follow company Aircraft Y on Taxiway 3; a company Aircraft Z behind the Aircraft Y will give way.The two aircraft; Aircraft Y and Aircraft Z were moving east on taxiway 3. As Aircraft Y began to pass; the Aircraft X Captain(PF) began to add power and roll forward to make the turn onto Taxiway 2. About 45 degrees thru the turn it became clear that Aircraft Z wasn't going to comply with the understood instructions as it continued to taxi east on Taxiway 3 past Taxiway 4. The Captain stopped the aircraft to give way to Aircraft Z. Once Aircraft Z was clear the Captain continued to roll forward on Taxiway 2 until Aircraft X was positioned on taxiway 3 but still about 90 degrees left to complete the turn as there was not enough room behind Aircraft Z to complete the turn on to Taxiway 3.Several minutes later Aircraft A was traveling east on taxiway 3. When aircraft A passed Taxiway 4 it became clear it was not going to stop and a possible collision might occur. The Captain transmitted Hey; Stop." over the ground frequency and the Aircraft A came to a stop. Then the Captain informed ground control of the conflict. Before the ground could respond Aircraft A came on frequency and said; "We were cleared to proceed!" Simultaneously Aircraft A proceeded off well left of the taxiway 3 centerline near the RWY XX L holdshort at Taxiway 5. Still well left of centerline Aircraft A proceeded around the nose of Aircraft X. The wingtip was approximately 10' in front of the Aircraft X nose making the Aircraft X crew extremely uncomfortable with the distance between aircraft.Ground control didn't appear to have situational awareness of what was happening most likely due to the proximity of the control tower to the area where the two aircraft were located.All aircraft then took off normally in the new order. Due to operational tempo it became impossible to debrief with the pilots of Aircraft A or Ground control.Cause: Ground Control situational awareness to the hold short area at XX L is difficult due to the tower location. Sequence not given to each aircraft. Aircraft X is a long aircraft and from gate XX it has to push onto taxiway 1. When assigned taxi on Taxiway 3 to XX L the turn of 180 degrees is challenging. Managing thrust and momentum on a heavy aircraft thru the turn was more challenging due to the multiple sequence failures."