I am right there with ya on the electric heat for the interior. Mine uses a Zerostart cabin heater. Plugged into shore power it keeps the windows defrosted and ready to go at a moments notice. Important for a first responder. I can use it for camping too if I need to. A little 900w generator will run it.
AC is a different story. I went with this one:
Champion 3400 dual fuel.
2000w was not quite enough to run the
portable AC unit when it is hot outside. It was working it hard when it did run the AC. The 3400 doesn't work hard at all. Better to be a little over sized for the demand , than undersized.
It is electric start. Should not be too hard to add a remote start relay If I needed one.
I added an an adapter , elbow and muffler to direct the exhaust upward. Works great and quiets it just a little more.
I have had good luck with Champion. Our back up power for the house is a larger Champion. It has been a great back up power supply for years.
We like the Propane option. That is our back up plan fuel. That made the dual fuel generator our choice. Given your needs how about this one:
Champion 3100 w/remote start
Notice that it has the correct RV 30a plug for a trailer connection. That is nice. No adapters