TL;DR:
Don't give your kids everything they need, but give them the tools to craft whatever they need! The most value stuff you can give them, is info.
As always: it depends.
- How large is the freezer exactly? I'll assume circa 2 cubic meters.
- Is the treasure meant as start equipment for a settlement, or for a journey? I'll assume first, with some equipment for looting tours.
General definition of what is needed. This has not necessarily to be included in the treasure. I'll try to sort the things, depending on how quickly the lack of these things will affect your survival. It does not mean, that lower stuff in this list, is less essential.
- Food/Water supplies
- Medical treadments
- Fire
- Clothes, depending on the area
- Orientation
- Crafting tools
- Info / how-to guides / ...
- Self defense
In general, dad has to give his kids the ability to craft what they need, instead of giving him the stuff directly.
Food/Water supplies
Situation overview:
There is plenty food for, at least, a few days. Depending on the kind of apocalypse (how many people are left?) it might be enough for days, for weeks, for years.
In any case, there is enough food for some days. The fridge isn't big enough to store food for years, so this is no topic.
But is there anything, which doesn't require as much space as actual food, which helps getting food or making stuff save to eat/drink?
What stuff should be inside for this topic:
Water purification tablets. In general, it's better to filter(@Info) and cook(@Fire) the water, due it doesn't waste tables. But in some situations, cooking is not possible.
A few cans of some food with really high calories. Pure butter or such. This is meant for really(!) bad days, just to prevent starvation. This should not taste good, to prevent the kids from eating it without really need.
Bottles aren't needed. There are plenty polyethylene bottles in the world which can be used.
A small pod for cooking(@Fire).
Medical treadment
Situation overview:
Medical threads are various. They cannot be foreknown. But there are some, that are relatively common and which can be prepared.
Problem is: Most medical equipment is one use, like antibiotics. These will be rare in some time and hard to find.
Due this, they will be very expensive in trading. Due they don't need much space, a relatively large stock is a good idea.
Even if their effect lowers over storage time, ineffective antibiotics are better than none at all.
Due their high value, they will also be perfect trading goods if anything is really needed to buy.
What stuff should be inside for this topic:
At least a shoe box full of:
- Antibiotics
- Painkillers which do not affect ones perception (Not opium or such)
- some hollow needle and scalpels
- A few (not much) dressings
- tourniquet
- surgical mask and gloves nd to prevent infection while threading someone who is ill
- Hydrogen peroxide as universal desinfection for wounds, surfaces, hands,...
Dressings should be multi use ones. After use, cook them. A belt can perform as a tourniquet as well, if none is there.
Never throw the gloves away, unless they're broken. Reuse them after desinfection. If you have to desinfect something heat resistant, save the hydrogen peroxid. Better use fire for desinfection then.
Some red poppey seeds to grow own painkillers (opium).
Fire
Not much to say here, ugh?
Several lighters, matches and flints don't need a lot of space.
Having 100 lighters in spare is not a problem and should be enough for a livetime, unless the kids smoke, which should barely be possible in this situation.
It's not a problem to craft a cooking place out of scrap, so actually, nothing else is needed.
Clothing, depending on the area
Situation overview:
Clothes have several purposes. They keep the kids warm in cold condition, dry in rain, camouflaged if they have to hide or good visible if needet.
Clothes tend to break while in use. It won't be too hard to find replacement.
However, the kids have to be able to repair their broken clothing.
What stuff should be inside for this topic:
- Sewing equipment. This needs nearly no space at all, so put a lot of spare (thick)needles inside.
- Buttons are multi use, however, they can break. Some spare buttons are a good idea.
- Tough yarn. It doesn't have to look fancy, but to hold the stuff together.
Orientation
Situation overview:
It's impossible to have everything needed on stock. It will be necessary to go on journeys or maybe to move. However, it will come to a situation, where the own knowledge of the area will not be enough.
Are satellites affected? Hope no, due they're completely independent.
What stuff should be inside for this topic:
- GPS-Devices. No kidding! If the satellites are working, there are no better alternatives for orientation then GPS + map.
- Maps, of course. Several ones. The local area, the region, nearby regions, the state,.. and so on.
- Mark known fruit trees on the maps, your kids will thank you for that info.
(Crafting)-tools
Situation overview:
This topic is too obvious to think about everything included.
What will your kids need to craft? Which tools are useful, which are not?
Any tool whit batteries, which is also available without, should be taken in the "no-batteries"-version. For example an electric screwdriver, better give an normal one.
Tools might be needed on looting tours, to open doors, boxes, and so on. So for some tools, there should be a second one which might not be as durable, but lighter.
For each tool, you should ask yourself: Can my kids repair them if they break? Can they craft new ones?
For example: The stick of an axe will brake eventually. But the blade of an axe is one of the toughest tools you can imagine. It's almost impossible to break it, without purpose.
What stuff should be inside for this topic:
- One axe + 2-3 blaces (Without stick, to save space. Sticks can be crafted easily)
- Shovel. Same as with axes, it's hard to break the shovel itself but the stick will break.
- Pickaxe
- Knives, several.
- Grindstone
- Woodsaw
- Metalsaw + spare blades
- Files in several cuts, can be used to craft new tools out of scrap. Files are some of the highest value tools of all due you can use them to craft almost any tool with them.
- Wire. Universal reuse material.
Self defense
Situation overview:
People will try to raid your kids.
While some people say a gun + ammo is not a good idea due ammo uses up, I think a gun is a very good idea.
You kids should not use the gun for hunting or raiding, because ammo really uses up. But as self defense tool, a few hundred rounds will be enough.
There is simply nothing else, that can defend you from raiders as good as a gun.
Also, setting up some traps and signs which say "Do not enter, we have guns and use them!" are a good idea.
What stuff should be inside for this topic:
- Some pistols
- Some hundred cartridges
- Axes are already mentioned in tools
- Some wire to set up traps
Info / How-to guides / ...
Situation overview:
Well, this is one of the biggest topics of all.
Your kids will have to know how to plant crops, how to craft this or that, how to fish, how to build a shelter, how to repair stuff, ...
Actually everything you can think about can be usefull and it's almost 100% sure that you can not think about everything they will need.
What stuff should be inside for this topic.
How to:
- cultivate plants
- craft tools
- generate electricity to recharge the batteries (GPS)
- craft gunpowder
- build a shelter
- sew
- build traps for animals
...
Can't list it all and as I already wrote, you probably can't think about everything.
Tell your kids, where they can get info. Where are libraries nearby?
And one point which is not be mentioned often enough, in my opinion:
- Elaborate a chiffre. The kids will have to place some reminders for themselves, like the location of stuff they buried. No one else should be able to read these information.
But the most essential part of all:
Tell your kids how to behave!
To be stingy with everything that uses up.
To avoid conflict with other people whenever possible.
Hide stuff at several positions.
Set up honey pots. Dig holes and close them again, without putting something in. People will open some of these stashes and eventually give up and search somewhere else.
Don't trust others, unless you know them for at least several weeks or months.