Stan,
Wow, this is like the Holy Grail of RV electrical problems.... Stan, you are doing a very good job of providing information and experimental results that we can go on.
What we know...
We know that there is only one condition that induces the fail, generator running, generator powering the coach AC wise (transfer switch closed using generator side), main slide switch activated with 12V and slide moving.
We know that the slide 12V side has no interruptions and runs well electrically and mechanically on battery/inverter not inducing any abnormally high 12V loads.
We know that the generator and transfer switch work well and can handle the load of two ACs, so having the normal slide 12V load added to any inverter charging load should not cause any overload current issue to the generator.
I think we know that the slide stopping issue is AC load induced with a 60 amp (or more) overcurrent when running just the generator. I think this overcurrent is also causing the inverter charger to shut down. This piece is a bit puzzling in that the batteries will run the slide slowly without the inverter normally, so somehow the DC side seems affected, I think pulled down with lower then 12v output stopping the slide. At the same time the solar charger DC voltage seems to get wonky during the slide movement activation/stoppage. That voltage may be seen on the output side of the solar charger but may arrive at that point from the chassis side of the wiring.
If we go on the physical movement of the slide inducing the fail (short or lose connection maybe) and not a load issue, as Gerald and Steve proposed, then what is the movement link? Stan, where is your generator located on your coach and is there any generator AC cable movement when the slide moves? Is there any AC wire/cable being pinched or crimped by the slide movement? This is a very good possibility with physical movement.
Either with movement or without AC wire movement, can you, with all power off, remove the cover where the AC wiring goes into the genset and check those connections into the terminal block from the genset side and the coach side for tightness, corrosion, or shorting. Due to generator vibration these terminal block screws can loosen and the copper wire can crush some with age being a soft metal and leave the connection less mechanically secure. Just moderate pressure on these screws, do not "crank them down". Then follow that AC wire from the generator and the other end should have wire nut connections in a metal box that also needs to be verified as tight corrosion free and the wire nuts should be taped or retaped when done checking. While looking there is usually a metal screw clamp to hold the AC wires, make sure that has not been clamped so tight that the Ac wire insulation is compromised at the clamp. My thinking was that if the genset can run two AC units then the AC wire connections were in pretty good shape but that is true for just the load and neutral legs.
Perhaps a loose ground from the genset end could allow the chassis and frame to "float" voltage wise causing the charger to erroneously kick in pulling major current from the batteries and that kills the slide movement. Check both the generator AC ground wire and the DC ground wire for good connections and also the ground and neutral wires at the transfer switch (along with the other+sides) for solid connections. If the voltage from the charger spikes up due to the ground reference voltage moving, the batteries are a very low impedance and can absorb or provide a lot of current which may be where the 60 amp 120V AC load is going. I cannot think of another place that current might go without burning something up or ruining what is already a loose connection. The slide coming to a stop on the DC side, which should be independent of the AC side, needs to be explained with a cause as part of this problem.
Stan, I read your post last night but decided to sleep on it....this problem is really a puzzle. If there is no AC cable movement with the slide movement, due to where things are mounted, then we are probably on the right path with some ground or neutral connection issue, given that the Alladin data has both the AC (current) and DC side (voltage) affected.
Checking the connections discussed is not wasted time even if you find them tight. Last summer I had one of the + side generator output wires come loose and we lost one AC output leg in the coach due to generator vibration and a partially stripped terminal block screw being over tightened at some prior point in the coaches life. Hope this helps.
Later Ed