Chamonix AND Zermatt?

Both places are truly spectacular in their own way - there are some similarities but I think they are each unique.
Going up the Aguille du Midi is one of the great gondola rides of the world and not to be missed. Across the valley I also highly recommend taking the lift up and hiking to Lac Blanc. It's one of the best alpine views in Europe with a refugio where you can sit out on the deck and marvel at the view of the mountains and glaciers across the valley.
Zermatt also has one of the most stunning gondola rides anywhere. Take the cabine all the way up to glacier paradise - I still think that stringing a cable line to that spot is nuts. I can't even describe the sheer massiveness of the surrounding peaks, cliffs, and the snow packs clinging to them. Just wow.
I really do think the Matterhorn is worth the visit - get off the glacier paradise gondola at Schwartzsee. The Matterhorn towers above you and there is a mountain refugio right there that has an outdoor deck where you can have a beer and enjoy the view! Then hike past the lake, up the ridge and get up to the old ski lift hut that is now inhabited by the cutest sheep you'll ever see - your daughter will be glad she hiked up there if for nothing more than seeing these cute little guys! It's not a long hike and once you are there the Matterhown looms above you - I, like you, was not sure I'd be very impressed but I truly was. It's a magnificent piece of rock.
I like the town of Chamonix much better than Zermatt. Zermatt is uber-touristy and uber-expensive. The lower part of town is newer but there are some parts of the upper town that are made of very old chalets that have been there for over 100 years. Between parking, the train into town (which you have to take), our lift tickets, food, etc., it was a $600 day - and we didn't even stay there. I did think it was entirely worth it though - it really is spectacular.

I really appreciate your input, Anita. You've definitely helped me see that Zermatt is worth the trouble. Thanks again.

If you can handle last-minute room bookings, you might watch the weather and choose while there. Consider the Bernese Oberland too - Jungfraujoch, Shilthorn, etc.

"For those of you who have been, is the Matterhorn /really/ that special? " Yes. It's the most stunning mountain I've ever seen.

"However, as many of you know, Zermatt is out-of-the-way, and I am spooked by stories of people who did travel to see Zermatt, but did not see the Matterhorn due to weather." I'm guessing those people only traveled for one day and got hit with bad weather, which can happen anywhere in the Alps if you don't budget enough time at each location. The trick is to give yourself at least three nights, which allows for two full days, and to avoid traveling in the shoulder seasons, which tend to be cloudier and wetter.

The hiking above Zermatt is also some of the best I've ever experienced in the Alps. Even at very high elevations above the valley, the peaks still soar far above your head. It's really spectacular.

I did enjoy both Chamonix and Zermatt in the same trip, having had time for both, without being much of a hiker. It sounds like you also do have time. If you trade it for something else, you will enjoy the something else, but will still be curious about Zermatt.

There is a small cemetery in Zermatt with graves of some of the men who died climbing the Matterhorn. Some of the graves' headstones have the daring young men's climbing tools attached. Sobering.