I can't imagine it would make sense economically to ship things like shampoo, when you can go buy a new bottle for a few dollars there. Travel size bottles that you've accumulated from motels work great, and then you can just toss when done.
Also, shampoo can be used to handwash items and as body wash. Conditioner can be used as shaving cream for shaving legs.
The first time DH and I traveled together we went sailing for three weeks in Greece-had to fit everything into our tiny berth so we each just took one carryon for the whole trip and a backpack. A lot of the room was taken up with books

. It worked out just fine, and was very freeing (and we had no washer or drier).
I have children, too, and know this is more complicated with kids, but I think it can be done, esp if you have checked baggage to work with. I could definitely do 7-9 days at Disneyworld with one suitcase for the two girls and me (they are 2 and 11) and one for DH that would include room for return souvenirs, etc.
Check out the travel stores, like Travelsmith.com, if you have the money and inclination to invest in some good travel clothes. You can buy things like quick drying underwear and wrinkle proof clothes. It is definitely worth investing in those vacuum travel bags, that you suck the air out of so the clothes are packed tight. Roll everything and pack it in tight. Pack shampoo, etc, into a ziploc bag. If you don't need the whole bottle of something, repackage it into something smaller (make sure to bring the original bottle for any prescriptions, though). If you don't need to buy it here, don't-get it from the store down there.
Here's what I would do:
-Each person gets a swimsuit, three pairs of underwear, three pairs of socks.
-2 shoes each; something like
Crocs or tennis shoes and nice looking sandals that are also good for walking but would work for a dinner out.
-Girls would get one comfortable dress or a khaki skirt; something that could be worn in the parks and on nights out.
-Depending on the weather, two or three "bottoms" for each person; shorts or long pants (probably three for the toddler)-like two pairs of shorts and a pair of nicer capris or long pants for evening or dinner out.
-Also depending on the weather, a sweater and a light windbreaker for each (one of these can be worn on the plane as it's always too cool there, I think).
-3-4 tops for each. Go for easy-care, of course. A couple of nicer tank tops and a couple of tshirts, with at least one being a little more formal (solid color, nicely shaped) for nights out.
-Make sure the colors all mix and match. If you're inclined, grab a couple pieces of jewelry that will go with everything.
-Add the extras for your family-a hat each, books, whatever.
I also find it helpful to think back to recent trips and try to remember what I took that I never used-usually, I wear the same few things over and over and the rest sits in my suitcase "just in case".
And if your girls are anything like mine (well, my husband is this way, too), make sure to supervise the packing. My 11 year old will pack fifteen shirts and no pants if I don't watch closely.
Last trip to Hawaii we had a condo, but I wanted to save a bit on their atrocious grocery prices on Maui, so I did bring some food with me. Mainly spices, so I wouldn't have to buy full bottles, but I also stocked up at Trader Joe's on snack food like dried fruit, energy bars, nuts. They are pretty light weight and, if you take the bars out of their boxes, are easy to tuck in with other things.
I also know that I tend to overpack if I'm doing it at the last minute, because I'm worried I'll forget something and so just throw everything in. You're being very planful by thinking of this now for next January, and I think that will be a huge step.