DIY storing family DNAs' samples for future uses (eg medical)
If you have access to a laboratory (or at the very least a centrifuge and pipettes) and some laboratory experience you can extract the DNA from the cells which would be much easier to store. There are a number of commercial DNA extraction kits available that are easy to find on google and order online. I don't want to promote any particular brand but I've mostly used DNEasy made by Qiagen (really just because that's what I'm used to). All the step-by-step instructions are in the kit and all the reagents are also in the kit with the exception of 100% ethanol which should be easy to obtain.

If you have significant molecular biology experience and access to a full lab with a fumehood and appropriate safety installations you can try a manual extraction using trizol or phenol-chloroform. This would be slightly cheaper however given the toxicity of these agents I wouldn't recommend this for you. It really doesn't sound like you have these resources available to you.

Once you have the DNA extracted you can dilute it in Tris-EDTA or the elution buffer that comes in the kit. You can store extracted DNA in a regular fridge (4C) for several years. If you're looking to store for decades you may want to rent space in a -80C freezer but this would be more expensive. A fridge may be just right to suit your needs. You should be careful that this fridge has a backup power supply.

I should be clear that although extracting DNA is the easiest way to do this for somebody with experience, you should not try if you don't know what you're doing. Some of these reagents are dangerous and you are likely to ruin the samples you've taken from your family members and end up with no DNA at all. Good luck!