The Fischer RX-6 has a wide performance envelope. It has much more performance built into it than many "intermediate" skis and it's certainly no noodle.
If it were me I'd likely go with 170cm. At your height and weight I think 170cm will likely work very well for cruising around in MT on mostly groomed runs with the wife and kids at moderate speeds. I know of good skiers who ski on the RX-6 and like it a lot.
The Fischer RX-6 is a carving ski intended to be skied in shorter lengths which is probably why the shop guys recommended 165cm for skiing with the family. Its sidecut is about mid-way between the Fisher RX-8 (Slalom carver) and Fischer RX-9 (GS carver). While I respect the shop's recommendation, I think that a 170cm length will work a little better all-around and still be easy to turn at moderate speeds.
I wouldn't go longer unless I intended to do a lot of fast GS type skiing or was a lot heavier than you are. If I wanted a high speed GS race carver, I'd choose a different ski in the Fischer line. I think that The RX-6 @ 180cm length is overkill for skiing with the family at moderate speeds and will be not be as easy to carve turns with or be as responsive as a shorter ski.
I'm a little shorter and lighter than you but am familiar with Fischer skis generally, and the RX-8 and RX-9 personally, though I've never skied on the RX-6.
Good luck with whatever you decide.