However, during a recent repair call the repair man reported that the dog barked constantly and that the apartment smelled strongly of dog poop. 

I’d have the regular heat looked at while the repairman is there as well.

He lives next door and checked on it himself then called the repair man.

This brand has a larger base of repairman, plus our dealer has a service arm. 

The repair man in me hates to remove things but the investor side is telling me its probably the right move. there is a 2 car garage with the property. 

Take the list to your repairman and have them address it quickly and appropriately.

If they cannot be repaired, have a repairman state that on an invoice as backup before charging them for new. 

If the refrigerator breaks (happened this week), you call a refrigerator repair man.

I feel that most of the maintenance issues that come up even here in my hometown, I don't have to be physically at the house to work with repairman, so could I do the same from out of state?

Since they’re both not working I’m thinking it’s probably not worth having a repair man out since the fridge is pretty old.