We have Spay Neuter Programs in our area that provide free or low cost Spay /neuter to those who cannot afford it. Maybe you could do a search for something similar in your local area.

If you think she will be moving soon and unable to take the cats with her you may want to help her get as many spayed/neutered and adopted as possible before she goes. Unfortunately most shelters do euthanize and with those numbers it is unlikely they would be able to take them all in one go especially since you say you live in the country.

Try and find a good rescue group in your area who will be able to give you advice on how to deal with the problem. Most shelters are totally donation funded so they may not have the resources to take the cats but most are willing to offer advice.

If the younger cats are sociable then they stand a better chance of finding a home, the sooner you can get them spayed/neutered the better their chances of finding a loving family.

Our local Spay Neuter Program offers Free S/N to cats under 6 months who haven't had a litter and is as little as $5 for a cat over 6 months/ or has had a litter.

If there is anything I can do to help let me know. If you need advice on listing cats for adoption, making your own website with pictures and bios or anything else web related just shout