Sounds like your dad plugged the PD 9155 into the inverter for some strange reason. It would not work out using the inverter output to charge the batteries, but the inverter takes power from the batteries. Maybe he thought the solar was enough to compensate. Hard to tell what was in mind.
At any rate, before you do anything, I would simply replace the batteries. Sounds like they are 6 volt golf cart type. Plug the PD 9155 into grid power and see if it seems to work to keep the batteries charged.
Leave the Trace 2012 in place for an inverter, but shut it off when not using it. It was a good unit and still probably works fine once it has a proper 12 volt
So, new batteries are the first step. Only then you will know if things are working properly. You then can evaluate the PD 9155 (a good unit too) and the Trace inverter. I bet both are just fine.