Though this only lists two resources. I would call both of them even if they're not in your area and ask for referals to more local shelters, SPCAs, generous vets, etc.
Also, do a search in petfinder.com for any listed shelters in your area and give them a call and see who they use for their spay and neuters, and see if you can get a certificate from them to get your 3 done. If none of that pans out, start calling your local city/county shelters and see what they can do to help you. Most of them should have a vet on staff or a list of vets they use and again, they may be able to give you certificate for a low cost spay/neuter.
Remember when dealing with rescue's, that most people who work there are volunteers and they're probably understaffed. You may need to call several times to get to real person, or to get your phone message returned. This doesn't mean they don't want to talk to you, it just means they're having a hard time dealing with the volume of calls and it's really easy for people to slip through the cracks.
Until you've got people snipped, no one can go outside. If mom or sister start showing signs of being in heat, then they need to be separated from the boy until they're all fixed. If he starts looking like he's trying to mount either of them, same thing, seperate until all of them are fixed.
I hope those will be of some help! Let me know if you need more info and I can see what I can find.