First things first: do you see any orange wires, or wires with orange tape on them? If so, you definitely have what is known as a "high leg" or "wild leg" delta system -- based on your voltages, I believe you have this, which was used historically to supply both 3 phase 240VAC and 1 phase 240/120VAC to mixed occupancies, as in the illustration below (courtesy Wikipedia/Gargoyle888):
In this system, the secondary center tap forms the split-phase neutral, with the A and C phases as the normal 120V "hot" legs in the derived split-phase supply, and the "high" or "wild" leg, while normally the B phase (this is from 408.3(E)(1) in the NEC, by the way) sits unused as it has 208V to the neutral on it.
Now that that's explained, to answer your questions in turn:
Typical 6/4 service entrance quadruplex uses PE (XHHW) insulation rated to 75°C and is thus limited to 60A. If you can confirm that the service entrance uses XHHW-2 (XLPE) insulation, though, you can run it up to a 90°C rating, which gives you a 70A (some sources say 75A) max ampacity. The XHHW or XHHW-2 designation is part of the markings on the insulation, by the way.
Is the ALU#4 cable type SE(R) or type USE (also called SEU) cable? SE(R) cable can be used for feeders indoors provided that the bare conductor in the cable is used only for equipment grounding purposes, as per 338.10(B)(2), or if all wires in the cable are individually insulated, as per 338.10(B)(1). However, USE/SEU cable cannot be used for indoor feeders as per 338.12(B)(1), as its insulation is not flame retardant.
Connect the feeder cable to the feeder breaker (either 60A or 70A) in the three-phase panel; connecting a load directly to panel busbars is simply not cool.
While your thought of making it so the subpanel main breaker trips before the feeder breaker in the main panel is appreciated, selective coordination is a much more complex piece of work than simply using a smaller subpanel main breaker than the feeder breaker. Here's an article on the topic if you want a taste of the gory engineering details that you'll have to work out to do this. You can use 60A breakers for both the feeder and the subpanel main, by the way; however, there are no guarantees as to which breaker trips first into a bolted fault (hard short).
You can tap the A and C legs from the existing 60A three phase breaker in the main three phase panel and use them to feed the subpanel; this is the most cost effective approach, and doesn't require any inspection of the service entrance conductors.
Finally, keep in mind that 60A is a very limited amount of current for a single dwelling unit. It can be managed, though, if you are able to run the heavy single loads (dryer, range/stove, hot water, and HVAC) using whatever fuel gas supply is plumbed to the building instead of using electric heavy-load appliances, or if the heavy loads for that dwelling unit are run directly from the three-phase supply -- although in some high leg services, the B phase is limited to a small fraction of the total load, which can make this infeasible.
Is there a reason the utility won't simply replace the obsolete high leg delta service with either a 240/120V split phase or a 208Y/120V three phase wye service?
Addressing the conduit problem, the neutral, and the balancing issue:
I would use conduit bodies instead of elbows, unless elbows are the only thing that fits in the space. In any case, make sure you have no more than 360 degrees of bends between your pull points!
The neutral coming from an overhead pole is on the bare wire in a triplex or quadruplex cable, just about always.
Phase balance isn't typically worried about in high-leg deltas; it's a concern in a wye system due to unbalanced currents flowing through neutrals, which need to be sized appropriately to carry it.
Alright your question is all over the place. Let me try to figure this out.
You have a three phase panel. The different legs are all 120V when measured to ground. But if you measure between any leg to another leg you have 208V. In that panel you have no neutral wire. Just three hots and a ground? You cannot just say that the voltage was 120V on the bus bar without saying what you measured it to (to another leg or ground or what?)
Are you sure this is a three phase panel. The 208V measured from Hot to Hot indicates that it is but do you know how to tell? 3 phase is usually only found in commercial and industrial sites. Not in houses.
What is this box that the white wire goes into thats adjacent to the pole? Does the power go from the outside overhead lines, to a meter base (where power is measured and reported to power authority?) and than to your three phase panel?
Are you now trying to make your own 60A single phase sub panel from your three phase panel? I am still not sure if you understand how 3 phase works/is. We can help you but you need to be more clear.
I am not sure what PE wire is and I am not sure if you are talking about the main service conductors here when you are wondering. But XLPE has a clear almost like shrink tubing around it. If you were to scratch the outside of the individual cable it would sort of rip the outside. Kind of like it had scotch tape on the outside and you scratched it ripping some up. It should also say in writing on the cable XLPE if you can see any writing.
Balancing your panel just means putting the same amount of power on each phase if you can. So if you had 3 big assed air compressors, you would try to put one compressor on Phase A, one compressor on Phase B and one compressor on Phase C. (Or on Phase A+B, Phase B+C and Phase C+A if they are 208V). Do you see. So you just try to evenly space your big loads if you can. The smaller loads you don't need to worry about as much. But if you were doing a sub panel you would put the sub panel on a leg that doesn't have very many big loads on it in the main panel.
If you have two 60 breakers than on a short would trip the breaker that responds the best. Thats anybodies guess. Is your main panel a 60 A breaker and you would like your sub panel to be 60A? Or is the load your adding 60A and the main breaker is only 60A?
Yes you can use 2, 90 degree elbows together. Depending on your cable size it could be hard to pull through if you did them back to back. If you could put a short strait section between them it would be better. Would 2, 45 degree angles work in this application. Its not as harsh on the corners to pull through. Unless your cable is small compared to the pipe and than it shouldn't matter to much either way.
So you are missing tons of information. Let us know.
Best Answer
The answer depends on the details of what loads are already connected to your 150A panel. You didn't say if this was a residence or other. Certainly a second 3-phase service would be highly unusual in a residence.
However, assuming that the sum of the existing loads on the 150A panel don't preclude adding the additional load of the guest house, then the 4AWG aluminum conductors would admit a maximum 60A feed (Unless you can find a 70A breaker… I've never seen one). Not 80A.
As to which panel to connect… if there are existing circuits in the guest house, I would be leery of connecting the SER to a different panel than these circuits… mixing circuits from two different services in the same dwelling is increasing the chance for disastrous errors in the future.
And unless you're really experienced, knowledgable, and qualified about electric power distribution, I would advise that you not touch the 3-phase stuff. There are numerous non-obvious pitfalls in that for the untrained person.