Welcome to the forum. I would neither upgrade the service nor add a subpanel. I would start troubleshooting why when certain eqpt kicks on it's causing the bedroom AFCI to trip. The bedroom lights (and others) will dim for a second due to inrush current when things like the AC compressor kicks on.
I would check the connections of the mains in the panel and the meter to make sure there is no corrosion, scorching, loose connections, etc that may be causing problems. Get a power logger, measure the voltage on the mains over a 24 hour period. Or just turn everything on and measure the voltage.
The size of the drop to the house on the PoCo side may not be sized correctly for the 200A panel; if it is small it will cause excessive voltage drop when high inrush loads kick on and exacerbate problems with the lights dimming.
The electric heat will not run at the same time as the AC compressors; it's one or the other. If both electric heat furnaces are running simultaneously, and with the cold weather everywhere recently, they very well may be, along with a water heater or both on, her 200A service is seeing quite a load. 150A dead load (both electric heat furnaces running wide open + 1 water heater) WILL cause some dimming of lights. The AFCI protected receptacles tripping is a different issue.
*eta: if this lady is elderly, she may very well have the thermostats set quite high (80*+). I'd inquire about that, it may give you a quick indication of how much electric heat is being used.
