If you really only have 5-6 days, I'm going to do something I rarely ever do and advise you to skip Beijing. Your situation is a bit unique, though. Mostly, you and the boys have been there before. If the wife is amenable to the alternative (she suggested, so she should be), then my plan would be a combination of Xi'an and Pingyao.

Xi'an: 3 days. With the following priorities, based on knowing nothing about your family except kids' ages:
--Warriors (don't overhype/overpromote in advance), and do the small pits 3 then 2 then the big pit 1 in that sequence, which is backwards of normal. Don't miss the chariots. You should be OK with 2 hours here, plus travel time to/from city. Afternoons usually less crowded than mornings.
--City Wall
--Muslim Quarter walk
--Big Goose Pagoda (water fountain/light show in Evening)
--daytrip to Zhouzhi Nature Reserve (pandas) (not the Changqing or Foping Reserves which are more for tracking wild pandas which is not congruent with a casual day trip visit). Few realize that pandas can be seen in the Xi'an area not just the Chengdu area. This needs a private car to get to/from.
--If the kids are OK with limited museum going, the Shaanxi Provincial Museum is one of China's better ones.
--Xi'an has a number of other sights that can fill 2 days in the city area (assuming 1 separate day set aside for nature reserve), you can research yourself and make up a B list.
--Most tourists are signed up for the Dumpling dinner and the Tang Dynasty Show, which might actually be fun for the family. Evening.

Pingyao:
--Surviving old town, spend two days is plenty (or afternoon + overnight + following morning is enough) .
--There is an all-inclusive ticket that gets you into a lot of the older buildings of note, but just wandering around especially evening and early morning when all the day-trippers are gone, is nice.
--City Walls. Think you can bike around on top of this.
--Get off the two central "touristed" streets--by walking about 10 minutes away from this, I bumped into an elaborate funeral procession taking place...not set up for tourists, just part of Pingyao life!

Xi'an I'd stay at a decent hotel, if you aren't using points or wedded to an international brand, then Bell Tower Hotel is pretty good and extremely well located by the Drum and Bell towers (surprise!). In Pingyao, book a traditional courtyard hotel in the old town, with kang beds, etc. Tian Yuan Kui used to be well-regarded and their restaurant good, not sure how they are now. I've stayed at Yunjingcheng since TYK was full--it was OK but it was also a few years ago. (Their restaurant was awful, though, eat elsewhere). There are also other places in the old town to stay and soak up the atmosphere.

Xi'an can be accessed by air or rail from lots of places. Pingyao is usually easiest to access from Taiyuan, which is about 2 hours away by bus on excellent road. Xi'an-Taiyuan is a route that has tortuous trains but usually really cheap flights (buy about 2-4 weeks in advance), so my advice would be fly between those two cities then take bus or if you have the cash, just prearrange a private car pickup at Taiyuan airport to take you straight to Pingyao. Taiyuan has high speed rail service (D trains) to Beijing in case you need/want to head there to catch a flight--3.5 hours.

With extra couple of days on your hands, I'd recommend taking the bullet train Xi'an to Luoyang and seeing the Longmen Grottoes. Other options in the area:
--Huashan Mountain, between Xi'an and Luoyang, also accessible in a bit over an hour from Xi'an by bullet train. Day climbs and overnights are popular, but it can be strenuous. Cable car service available also.
--Shaolin Si area, near Dengfeng between Luoyang and Zhengzhou. Martial arts (kung fu monasteries), but beware has become very touristy. Read up in advance so you know what to expect and aren't disappointed.

Highly recommend whatever you choose, to have you, wife, and especially boys do some advance reading on Xi'an and Pingyao, so they have some context of what they will see.

Finally, if you think this is all too much history on this trip, then perhaps 3 days in Xi'an/nature reserve + 2 days in Jiuzhaigou/Huanglong National park (north Sichuan province) is an alternative plan. There is air service between Jiuzhaigou and Xi'an, and much more frequent service between Jiuzhaigou and Chengdu. With one week, you could have a very nice Xi'an-Jiuzhaigou-Chengdu trip (last includes Giant Panda breeding center and also the Leshan Big Buddha). Flying into one of the big cities than out the other.