You have several options on how to run things.
What you are asking for is a bit off of what would traditionally be defined as multiple zones as this typically indicates the desire for multiple sources.
How to accomplish what you asked for...
1. The main zone - you have this figured out, all A/V receivers do this.
2. The secondary set of speakers (zone 2) - You didn't get into the nuances of zone 2 speakers, but if you want the exact same source in zone 2, playing at the exact same volume as the main zone, then using the B channel of the main output is fine. But, you will find that many mid-level receivers offer up zone 2 independent output with excellent control. Receivers such as Denon's AVR-2308 I believe cover this and include amplification for zone 2 as long as you don't run a 7.1 audio setup (use 5.1 instead). Otherwise, an external amplifier is necessary.
3. For the kitchen, I would get an external amplifier and hook it up to the 'RECORD OUT' of the A/V receiver. Then put a volume control in the kitchen where you want it. This works very well as it tracks whatever the current source is and is always 'on'. When you turn on the family room, the kitchen comes on, and the volume know adjusts accordingly. No thought at all is needed to make this work exactly as you describe. An external amp can be had online for under 100 bucks.