I have plugged in while parked at home since I have owned my 2004 sportsmobile, I just replaced the tripp-lite last year so most of my data is with the same inverter charger. I also replaced my battery last year so I am nor on my third, the first battery died early because of a shorted battery cable, so my battery life has been good.
A couple of things to worry about, you need to monitor what you're loads are for extended runs at float, there is a phenomenon where the charge can get faked into going back to absorption, when there is a momentary current spike (such as you're fridge coming on and off). This can result in overcharging if it does.
Battery Thermistor, make sure that the thermistor is hooked up to the battery, on the tripp-lite it is taped to the side of the battery, since you have replaced your battery make sure it is hooked up properly. Since you deal with large temperature variations you want to make sure the charger is compensated for the battery temperature.
(if you were counting on your solar charger to maintain the battery, it to needs a temperature probe)
Is your starting battery a wet cell or AGM ? If wet cell you may want to monitor you're water level, long durations of being at float will reduce water in a wet cell. Or you can make sure you disable the Surepower 1315 or Blue Sea magnetic latch relay if you have one, if you have a diode based isolator you should be ok.
I would also disable my solar charger for long durations of being plugged in. Solar chargers like to think they need to come alive every morning and this is where I have seen the Solar Charger force the battery level to be absorption, this is very similar to first phenomenon I spoke of I was able to track it to the solar charger
http://www.sportsmobileforum.com/for...her-16303.html
hope this helps.
-greg