During humid, wet days, the phases of our house(two units) electrical system drift from another. Both phases go to each unit. One phase might be 90 volts while the other phase is 130 volts. After a visit from the power company, it was determined we did not have a good earth ground. I've pounded in two ten foot copper ground rods, and am now looking for a good point to connect. The power company technician pointed to a good point in the meters to ground, but the meter now has a seal that I would have to break to access. There is a switch box below that has a ground point. Is this likely to be a good earth ground for the whole system, or is it a ground for just the enclosure? Pic below is of one of the fuse boxes below the meters
In North American split-phase wiring...
How ground rods must be
Each building must have its own set of ground rods. 2 rods are normally used, but they must be set at least 6 feet apart (catty-corner on the building is ideal). Ground rods must be connected to the GROUND bar of that building's panel.
If you have a meter stand with a main disconnect switch separate from the buildings, you need ground rods out there too.
You posted a pic of 2 meters with 2 fused pull-out disconnects immediately past the meter. That's your "first disconnect past the meter" and there must be GES (Grounding Electrode System) wires from there going to ground rods or equivalent.
Neutral and ground bonding
You have the weatherhead or other connection point where the power comes from the power company. Then you have their electric meter in your meter pan. Then you have your first disconnect switch or main breaker.
In your photo the disconnect is those fused pull-outs. Here is where the utility-provided neutral is bonded to your local ground bars. As of NEC 2008, from this point ground and neutral must be carried as separate wires.
YOur installation looks pre-2008, so I gather 3-wire cables were run from here to the regular breaker panels. Note that this installation is extremely ancient and you'd do well to replace it with a couple of Ranch Panels.
Phase imbalance? Related to ground? Not likely!
The power company has a transformer with 3 taps, like above drawing (ignore the left side). 240V across outside (2 to 4) and 120V in the middle (2-3, or 3-4). That's what forces 120V... ground has nothing to do with it! Heck, before 1950 houses weren't even grounded, and it still worked normally. So ground is a red herring they are telling you to "make you go away".
The utility must provide 3 wires - 2 hots and a neutral. High/low voltage differences between the phases is always caused by a neutral problem from the utility. This is so common we call it a "Lost Neutral" and we give stock advice on having it fixed (call the utility).
Grounds do not enter into it in any way whatsoever. Except that after the neutral has broken, ground becomes an "alternate path" for all that neutral current. So a healthy Grounding Electrode System will reduce the severity of the voltage swings. But they should not be happening AT ALL because the neutral should not be broken.
It is not appropriate to say "Neutral problem? Customer must fix their grounds!"
Mind you, you are not sharing all the details on your setup, so there may be stuff unmentioned.
One phase might be 90 volts while the other phase is 130 volts.
This the symptom of a "floating neutral". It is the responsibility of the electric utility to provide you with two live phases and a neutral. Since they lock the meter box, their responsibility extends to a connection point on your side of the meter.
If you are in the U.S.A. the fault ground for your house must be connected to the utility's neutral supply point at exactly one place.
I can't imagine why it became your responsibility to pound in two ten foot copper ground rods. If these are needed then your power company should be installing them.