Mom's Cafe Serves Everyone Extra Helpings of French Fries, Mustard, & Ketchup.
That's how I remember the 10 Essentials. Some schools of thought will tell you that you should only carry what you need, as extra slows you down. I disagree, not only personally but in your situation with a family, as almost anything can happen in the woods/desert/jungle/etc. With some fine tuning, this stuff can easily be fitted into a normal, school-sized backpack; I've gone extreme and put it all into a lumbar. I'll give you the basic, plus my own idea. Be advised that my list is a basic version of a 24-hour pack for Search & Rescue, so some of my stuff is overdone. I can still carry my lumbar as a messenger bag and not look too funky, though. Here goes -
1. Map. Obviously, this depends on where you're going to be. Most places that have lots of hikers will have topo maps for you. I've been playing in the outdoors locally for 20 years, so in my local parks I don't carry a map. When we're called out to areas that I'm not absolutely 100% familar with, I grab a map every time. If you can keep in it a waterproof map case, that's great, but a gallon ziplock bag works almost as well. .
2. Compass. Not the one that came in the McDonalds happy meal, either. I carry a Suunto MC-Something or other. I've got different needs being involved in SAR, but I'd say that anybody in the woods should have one. More than one, really. Many times you can tell direction from stars, the sun, yadda yadda yadda, but when you're completely confused it's nice to have something to tell you concretely where you are.
side note - GPS units are great. I've got one, I use it all the time, but by no means would I rely on it completely. TONS of people get lost using them, when the drop it and it breaks, the batteries die, you get the idea. Before you use a GPS, you should be able to use a map & compass. I'd never carry a GPS without having the backup. But back to the list.
Sunglasses & Sunscreen. Pretty standard stuff, really. My eyeglasses change for me in the presence of UV rays, so I don't even have to think about it anymore. You're out there enjoying nature, and nothing is worse than having to walk along blinded by the sun while your skin stings because of sunburn. I like to carry the little mini-tubes of sunscreen myself, I burn pretty easily and they're not too big, so I never consider leaving them behind because of weight or anything. A good hat is also nice, whatever you like, from tilley to boonie or even cowboy.
Extra Food. When my group goes out everybody carries their own food. My daypack has an MRE tucked in the bottom. Gorp is good, freezedried is good. I personally try to stay away from things that need cooked. This is also a good time to mention water. Everybody needs water. I carry a minimum of 2 liters of water, most people tend to only carry one. Whatever works for you.
Extra Clothing. Kinda seasonally dependant. A change of socks is nice, for when you slip and fall into the creek or something. Maybe a nice jacket would work for you. This is up to you, really.
Headlamp or Flashlight. I carry lights all the time. Even when I'm not in the woods, I've got 3 on me. I personally try to stay consistant with batteries, so everything in my pack takes AA's. I've got an LED headlamp (PT Matrix), Single-cell walking light (CMG Infinity Ultra-G) and a 2 Cell spotter (Minimag w/Terralux Ministar2 conversion). I have to operate in the dark fairly regularly, but even if you don't, you should have something just in case. If you didn't notice, all of my lights are LED, which sip battery juice. From my experience, I don't need a huge monster spotlight in the woods when I'm hiking. Some might, I'm sure, so you'll need to taylor this to you.
First-Aid kit. There's a ton of them out there. Be sure to remember any special medical issues (medication, formula for babies, etc.) when you're packing this. The key word is "First", and if there's massive injury most people aren't trained to do anything helpful anyway. But you'll be there first, so just have enough to take care of things to get you out of the wilderness, or to make the person comfortable. I can handle minor injuries with my training, with my kit and with what I find in nature. A good first-aid class is always an idea.
Fire Starter. Hopefully if you're hiking you won't need to stop and start a fire, but if you would, rubbing sticks together gets old after a while. I carry a lighter, matches, a flint, a mag bar, plus some odd tinder. It's good to be prepaired.
Matches. Hmm, I think I already said this, huh? I could add on those trioxianne bars, maybe. I don't carry them myself, but some people do. Maybe parafinn paper??
Knife. I carry 3 when I'm not in the woods, a BM910, LM Micra and a cheepie SAK knockoff to avoid spooking the sheeple. In my pack I've got a Ti fixed blade and a SOG Switchplier, plus the ever-present SAK in my first-aid kit.
Like John-Boy said, give us some more information (like I haven't rambled on enough already), and I'm sure you'll get all the stuff you need. .