I have noticed, sometimes when I take off the shore power with the inverter/charger on, the inverter will kick in and out repeatedly until I turn it off for a few seconds. If I turn it off prior to taking off shore power, it won't do it, when I turn it on. Since I have figured out a work around to the problem, I don't worry about it any more.
Sounds like you might have had more watts being used than it could handle, try it again with just one of those devices on, and see what happens.
Monty & Janet - 2007 Alpine APEX 40 MDTS
S/N - 75715 - Retired - Master Certified RV Tech