I think I can relate to what you're feeling.
My husband and I take care of my mother-in-law, who is 90 years old and still lives alone. All her life, she's been very independent and sharp-witted. She's been a widow for the past 15+ years and in reasonably good health, considering. She has a pacemaker and asthma, which is well-controlled with medications. She broke her tailbone 5 yrs. ago, but it's healed up well and gives her no trouble.
She became 'visually impaired' 3 years ago, forcing her to stop driving. Ever since, I've been her chauffer everywhere she goes. I don't mind, because it saves us a lot of worry about her driving around. Understandably, she has declined steadily in her mental status & memory for the past few years. I manage her medications & dr. appts., but because she insists on living alone and trying to do some things for herself, she has made some dangerous mistakes - like mixing up her meds, too much self-medication, etc. As you can imagine, it scares the heck out of us. I also do all her shopping, manage her financial affairs, etc. We live 10 miles from her, in the next town. We can't move closer to her because of my husband's illness/disabilities. And she refuses to let anyone else help her - paid help or otherwise.
We're well aware that she also falls sometimes, and has other problems that she will not admit. She always has an explanation for bruises, scrapes. Since the broken tailbone 5 yrs. ago, she won't call us when she needs us. I've spoken to her dr. about all of this, and he asked her if any of it is true. Naturally, she denied it all. So he just dropped the subject and doesn't seem a bit concerned!
I know she's afraid we'll "stick her in the nursing home", despite all the reassurances we've given her that we will NOT do that to her. She's financially well-off, can easily afford a nice assisted-living facility, or at least some good paid staff. I think she's just afraid that someone, anyone, will see that she is no longer able to live alone. On the other hand, there are more & more days that she says to us, "I don't understand why I'm still here. Why doesn't the Lord just take me home?" She's outlived ALL her family, except her only son, (my husband) and grandchildren.
I can only imagine how hard it must be for anyone to admit to themselves that they need help for simple tasks and daily functioning. But we're scared to death that one day we'll arrive to find her on the floor, out cold. We see her everyday, she has LifeAlert, but that's not always enough.
You didn't say how old your father-in-law is. Has he been dx'd with Alzheimer's, or anything? Not that it matters - there doesn't have to be a diagnosis for there to be something wrong. Especially plain old aging.
Wish I had some answers, but all I can offer is "I can relate - been there, done that, still there." LOL
Hang in there and just know that you're doing the best you can to care for your loved ones, and it's all you can do. If you get any good advice, please pass it on!