mobilmike...
Some really good advice already, but you've left out some important details. Just how old and big are your young children. Can they carry 4lbs. each all day? 2? I'm assuming if they are 4 to 5 years old, you're only talking a couple of miles, tops? Depending on how focused they can stay? You mentioned going into country where bear cannisters are mandatory, so I'm assuming (maybe wrongly) if bears are a possible threat, little kids will be sleeping in the tent with you. Bigger tent - more weight. Will a spouse/partner/other adult be hiking with you?
O.K., it's already been stated that you should take a hard look at what gear you'll actually need. Look at that gear, and see if you can lighten it up some.
Are you going to camp at a base camp, possibly a state or national park camp, and take day hikes? In that case you can take anything you want, put it in a tote and throw it in the trunk, SUV, truck, whatever.
So, now that people have suggested taking a sincere look at your necessary gear, also think about (realistically) what kind of trip you're taking, your children's physical abilities, any special needs, that might mandate they stay close to a base camp (medical maybe). Maybe it's a bit to soon to be thinking UL while the youngsters are small, even though you can still cut every corner possible. Maybe you can buy them appropriate sized day bags, and stuff the very light but bulky items in them.
I kind of doubt you're going to be able to cook, heat water, etc with a 3 or 4 ounce stove plus fuel, for an adult and two children. Are your kids prepared to eat rehydrated meals? Oatmeal in the morning, yes, but those high energy little folks can get pretty hungry at night...you'd know this about your kids better than anyone.
I'm just not seeing UL and the type of camping/hiking you'll be doing with small children fitting together. If you're only going to be a few hundred yards or less from the vehicle, then you have no worries. I'm a little sleepy and loopy, but do you see where I'm going here. If you plan to backpack in, camp then pack out, I'd say just use your large pack, because I think you're going to be humping the bulk of the gear anyway, unless the spouse/partner/friend can split the load with you.

Invest in the UL stuff a little later, or now, for trips when the kids are at Grandma's.

Actually, I still haven't hit UL status myself, although I've been learning to cut weight over the last 15 years, more as I age, which is why I joined this Forum. But I stil need a comfy bag, and pad, and sometimes If I want to go for a week or so, a pack large enough to stuff everything in, regardless of how light I get it.

Good luck, and have a great time introducing your children to the outdoors. If they love it now, then they'll probably love it for life.

J.