Agencies are a huge part of the problem with getting someone to help at home. I had one agency owner tell me that of the $15 per hour charge, he gets $5. Can you trust a person that makes $10 per hour before taxes? I've heard of another agency that charges $16 and takes $8. You're not going to get a happy person taking care of your loved one going that route.
I am a primary caregiver for my 87 year old dad and have found a workable solution. He only needs companion help. He has early/mid Alz and gets very agitated and depressed when left alone. He can hardly manage to complete simple tasks any more. I've posted ads in the employment section at craigslist.com. I don't mention salary, other than that it's competitive. I say how easy he is to take care of, including his cheerful disposition, and list job responsibilities as keeping him company, running errands, light housework, etc. The responses come rolling in. The two times I've done this, once in Florida and once in NJ, I've found young mothers who need extra income. They do the basic stuff on a flexible schedule for $10 per hour. Sometimes they bring their kid, which is good therapy for dad.
Just practice due diligence and make sure they are who they claim to be and take proper security measures (nothing of value, especially information, that they can access). I promise them a minimum # of hours per week, usually 25-30. After doing everything by myself for almost a year, I was ready to lose it. The new solution is affordable and a bonus is that I'm helping a mother and child who really need the help. They become like family members too!
Again, just be extra careful who you let into the home until you're sure about them. Young mothers tend to be honest because they've got a child and the accompanying responsibilty.