I understand that it is a power struggle to get my father to shower and changes his clothes, but how do I get him to do what he needs to do?

Stldaddysgrl and annet are giving good advice. It's not a power struggle unless you make it one. These men have been in charge and responsible for all their adult lives, they now have lost so much control and they are aware of their loss. They still need to be encouraged to do what they are able to for themselves and even for others.
What works for me, as a caregiver for my husband of 57 years, is to step back and walk away and give him a few minutes. When I return he has usually forgotten any disagreements and I take a new approach and it works. My LO is very frightened by his not being able to understand what is happening to him or even where he is and he needs lots of reassurance and love and patience.
The toe nail cutting is another real problem for us. He refuses to allow anyone else to touch his feet, including the professional, but winces and jumps when I cut the nails. His big toe nails have grown so thick that our best clippers will not penetrate them. I am going to try soaking his feet first to soften them.
Good luck in the patience department! pvrwilson

It must be maddening for you. My 90 year father did the same thing, refused to bathe and change his clothes. He was not capable mentally to do those things, my mother took care of him and we tried everything and he still refused, even his home health aide had no luck. My father has dementia and it got to a point where my mother was neither physically nor mentally able to handle him anymore. The only option for him was an Alzheimers facilty and even the trained staff have a hard time getting him to shower. But, he never once asked to go home, he adjusted right away.

My mom would not go to the denturist even though her false teeth were over 30 years old. I told her they called and made an appointment for her to come in and when the day came she got in the car without argument. It sounds like your dad needs to see a doc or nurse soon. I can talk till I'm blue in the face and get no reaction, but if the doctor tells her to do something, it gets done. Ask the doctor to tell him he has to bathe every other day (at least), maybe that authority figure will help.

Dad, I noticed you eat a little later than the rest of us. Would you mind if I make dinner a little later every night so WE could join YOU? Ball is in his court. He's now in control again. Also, I come right out and tell my dad he stinks when he says he doesn't need to shower. Dad, there's some pretty stinky smells coming from you... And my personal favorite.... D you remember (insert name here) from wherever? Well I ran into her today and her uncle, cousin, father whoever, had to have his toes on his right foot amputated because he refused to change his socks! Can you imagine that? How gross! then be patient and stand back and watch. I get my dad to do all kinds of things with This type of thing. He just wants to be in charge of some stuff now and then. Pick your battles. He has also told me I use my monster voice when I mean business. (I'll talk through gritted teeth) and he won't mess around then!

You might be better off not to view it as a power struggle but to take a different approach - not sure what but try and use imagination, that is what I do anyhow. Good luck.

I was going to suggest taking him to a podiatrist, but now that he has an infection he needs to see his regular attending physician. It's possible that it is time to have him live in an assisted living home since he won't cooperate. Maybe just the "threat" of moving out of his own home will get him to be more responsible. If not I'd enlist the help of your father's doctor. Good Luck.