The problem in this case is the Standby selection based on user's choice AND when a pump fails. Once that logic is set up, the other parts fall into place, using relay logic only and 3 timers in 15 ladder rungs.
The first part I did was to set up 3 rungs that use the selected Standby Pump to then alternate between the two remaining pumps (Standby Selection and Alternator Trigger to be determined). You can see that first rung I did in the attached sample picture, Rung 009.
I then built on that by adding the rungs to select the Standby pump based on 3 manual pushbuttons. Then I added the rungs for the Alternator trigger based again on a one-shot relay output that is selected with a manual pushbutton, or when the running pump fails and goes into Standby mode (Rung 000).
This one-shot relay then tirggers the alternator logic (Rung 007), which select the pump out of the two remaining possiblities.
I will add one of the Pump Output Rung 012, to show that I have not setup and individual Start-Stop pushbuttons for each Pump (recommended).
Again, post what you have done so far, so we can build onto it.