Hi, we are Aussie family that has skied Breckenridge and surrounds 3 years over the last 5 or so. I just saw your post as I was about to post about going to Mammoth. This year we are trying late spring skiing to fit in with our school hols.
November is early, so you may want to go where there is snowmaking as other posters have suggested.
We rented a condo all times, the last one just out of Breckenridge because after 2 visits we decided Breck was the place for us, with the easiest access. Kids were 4, 5 and 7 when we first skied, 8, 10 and 12 when we last skied. Peak 9 can get busy Xmas to NY but other than that just is really empty compared to Australian and NZ ski resorts. Peak 9 also has lovely easy kids runs, wide open and not very steep, in fact parts you will need to tow them toward the bottom if they aren't going fast. You can also just do the top part of the greens avoiding beginners at the bottom. Lovely cafe at the middle level of peak 9 for kids. Note that the Mascots - forgot their name... and the tree skiing will probably be not open in November for the kids... last time we were there in early mid December and there was no snow in the kids areas. Ah, I have remember Riperoo Forest, best kept out of by adults, narrow icy paths not made for long skis. Lol. Plenty of groomed snow on the runs though.
We usually fly into Denver and overnight at one of the hotels that has car hire. We get an airport shuttle to the hotel. We overnight to help with jet lag and also with acclimitisation. Next day pick up our big Escalade or whatever either at our hotel or by walking down the street to wherever it is. Lots of the hotels there have car hire. Drive up to Summit County and grocery shop and organise the skis and ski passes that day. As an out of towner you are going to have to get your photo done and pass made etc. I book waaaaay in advance to get a good deal on car hire and we get the monster trucks so that can just chuck all the gear in the back. I use vroomvroomvroom.com to book with no credit car / no obligation, if I find something better I take it. But the earlier you book the better. Going home we just drive straight to the airport and then either onto a connecting flight home or take a day at Manhattan Beach at the Marriott to just break the journey or airport hotel. Also allows a bit of leeway if there are winter storms and flight delays.
We don't bother with ski in ski out accommodation up there as it is so easy to access the ski resorts and park. Also early in the season some may be walk out , walk in. Even if you pay for the parking it isn't too expensive. Free parking at Breck is a little out of town but serviced by a shuttle. I like the car park at Peak 9 under the child car centre, ski down to Maggies from the car park or walk up the stairs to the the other cafe/lift, too easy. And you can ski to the car any time you like to get the lunches or other gear, no locker required. Keystone you have to take a Gondola up the mountain which can make coordinating the whole family if someone doesn't ski difficult. Suggest you get some US mobile phones while you are there. Your Aussie ones might work with a simm card. Makes it easy to coordinate stuff.
Breck is great as it is easy to get to Frisco and Copper, buses run to Keystone, and are free, but you might have to change. Breck and Silverthorne both have community centres with fitness and swimming. Breck has ice skating and a nice touristy shopping district, old Western style main street and plaster painting for Mum / Kids / even Dad for a day off. Just do it in time to get it fired and collect before you fly out.
We don't bother to eat out in any of the places there, lines are often too long, food is expensive and we are too tired after skiing, we just visit the grocery store and eat in. We also make our lunches and take them along, wraps and mandarins is the usual fare. If you take your own tea/coffee or hot choc sachet hot water is rather inexpensive to purchase at the ski resorts. 5 people skiing one month means we like to eat healthy and watch the budget. Take your own tea from Aus if you are a dedicated tea drinker, after 25 years in the USA working I still find it hard to find good black tea!
Silverthorne is a satellite town and has an outlet Mall - don't forget to visit their customer service and get the free discounts card from them before you shop then ask before you buy what the offers are. The US loves their discounts. Also has movies, fast food and some restaurants.
One thing to take into account for the amount of time you are there is the altitude. Visit your Dr and get some medicines like diuretics to take if anyone gets altitude sickness. You will be out of breath for a few days, and some won't adjust at all if they are unlucky. Also take into account that you will fatigue of skiing each and every day. If there is a lesson and season pass deal that sounds like a fantastic idea, but I try not to worry about ski lift costs as they are what they are. Better to ski where it suits you and I try and make up the costs other places.
Take very good moisturisers - the air is so dry you will all end up with itchy skin. Lots of condo's will have humidifiers for you to run. The upside is that the snow is dry, and you never have a problem getting your boots or woollens dry overnight, the water just gets sucked right out of them by the air. : - ) , As an Aussie ski Mum I nearly died the first time when I arrived and there was no drying room, how was I going to get six peoples stuff dry each night.
Get some Naselate or similar from your Dr, good for bloody and dry noses due to the thin air as well. It's an ointment used after nose surgery. In Summit you can only find aloe verae ointment or saline wash - sinusitus is a big deal up there with the cold dry air, but never seen Naselate and it is a good product. A GP friend put me onto it.
Re gear hire, go in and talk to the outfitters where you decide to stay, I once got a demo deal, unlimited hire up to 4 days at a time for $200 bucks for the season, for the adults and they comped the kids!!! I said, do I have to take the ski's out of the car when I rehire every 4 days and they just said, nah, don't bother, just don't keep them over a month. Next time I just went in and negotiated and got a similar deal with a different outfitter.
I use VRBO.com to hire condo's in the area, I have never been dissapointed. Again it is so easy to drive up there and park that staying out of the resort is not a problem. I like having space, washer/dryer and kitchen along with wifi and tv's and space to spread out in several bedrooms. Most owners will discount for longer stays and include the cleaning.
If you don't want to drive or hire car, I would suggest getting a transfer up from Denver to Breckenridge, stay in a condo on the shuttle route. You should be able to shop in town using the shuttles and also get around Summit Country. But it will be more time consuming that if you have a car and as mentioned before someitmes you have to change busses at the exchanges. Our nanny used the buses one year to go from Breck to Silverthorne to Keystone for night skiing and other days out and found it ok. If your kids don't like to carry their own skis you could look at putting them in ski lockers at the resort, if you are skiing them same place the next day.