Angeline,
There are a number of methods for preserving your grandmothers precious crochet work for the grandchildren. Even without a cedar chest, you can still purchase cedar balls and store in a plastic container. Although, these would not detour rodents.
My preferred method for smaller items (coasters and even doilies) is to make a mixture of equal amounts of Elmers school glue and water. Mix together well and pour on a plate or pretty flat bowl. Place your crocheted item into the mixture and squeeze to help the item soak up as much of the mixture as possible. When you're sure it's quite drenched you need to squeeze it out one more time and flatten/block on plastic wrap. When dry just store as above.
This mixture will easily wash out in warm water at a future date or it can be left in indefinitely.
If you're talking about large items such as afghans and shawls, I suggest the cedar moth balls stored in with your crochet items and placed in a plastic storage tub/zipper bag (such as comforters and some sheet sets come in. Then, place these in a larger container (maybe even more cedar balls should be placed around these also).
There are all kinds of little varmints; besides mice and rats to fear. There's the moths, roaches, silver fish, fire ants (depending on the area you live in) and a whole pascal more. It's best to confront your local area as to what best detours those specific critters.
Hope this helps you. If not, contact me via PM and I'll give you so me more ideas on storage and preservation of crochet items.