Dear Jim's daughter, hello and welcome to TP, and forgive me if my welcome seems a little harsh in the reading....
Fact is, you can't manage it on your own, unless you are a fully qualified professional with no emotional involvement. Brutal I know, but I suspect you didn't arrive here without being at the end of your tether and looking for some answers (none of us have them exactly, it's such an individual experience, isn't it?) or at the very least, support. There are people out there, in the System, who can help. That's what they are paid to do.
Are you receiving any support? GP first point of call; consultant; social workers to provide some respite for Mum (against her best wishes) to keep an eye on Dad's progress? You don't mention this so hard to know what to say. So if you haven't...
You, and primarily Mum and Dad, need some support so if you haven't already hit it, the System, hard and quick. The GP is the first port of call, social services for a chat to determine support and the other services available for respite, you will find this info from some of the contributers to this Forum, a lot of help depends on where you live!. The Alzheimer's Society has a variety of fact sheets and helpful advice and people on here have their own experiences to share. Use all of this, it can/will help.
If you go to the top of this forum and, where there is a Search facility, type in the words Chest/water infection, you will be amazed to read how common this problem is and how debilitating this can be for anybody, never mind an AD sufferer. It batters the immune system and leaves the patient very weak. This infection, on top of a water infection, will be devastating to the immune system.
You don't say whether Dad is on any drugs to treat the dementia, but I have a feeling that he isn't aware of his incontinence so of course he doesn't care. All social graces are out of the window with this awful illness and if you are drugged you won't have time to make the loo even if you are still aware of the need. Such is my experience, nursing my Mum.
I have to tell you, for what my ten pence is worth, that Jim must have been a loving man in his time to have such a daughter looking after his and Mum's welfare. Just don't 'lose it' when you are met with the testing obstacles of 'everybody coping alright without anybody interfering' and other such objections. Have a word with social services and the GP in any case, GP first. It will get Dad into the 'System' when you really may decide you need them. They can provide all kind of practical stuff, advice on bedding for the incontinent, help with bathing, etc, day care to take away some of the stress. Gently does it.....
.....and gently does it with yourself. People here are wonderful, helped me so much in the past. Never despair when you have this outlet for however you are feeling or whatever information you may need.
Kindest of wishes
Chesca