Is it wrong for me to not want to help my dad get dressed for the day every morning and get ready for bed each night?

Can the AM/PM chore be split with your sister close by? Or have your brother and other sister come a week at a time to give you a chance to get away on a vacation. Even doing this little bit will soon change their minds in a hurry about the extra expense. Your sibs MUST take on more responsibility if they refuse to pay for additional services.
If your Dad is 101, he surely can't last much longer, maybe a year to five years, and you have to think about your own future, too. Why are you only working one day a week? Can you not extend that to 3 or 4, and you would have the other 3 or 4 of duty.
All this is in lieu of not paying for the extra help.
I'm interested in the fact that the facility wants more $$ to do the work. How much a month would cover it?

So many excellent responses/support here. What an amazing network. It is easy to say "don't feel guilty" - I'd say, deal with your feelings by being really present with them (firstly) and reinforce its okay to set your own boundaries with 'time and duties,' by writing affirmations or doing visualizations - whatever works to transform any negative associations - with this particular task. If you feel good about yourself and what you are doing, that will come through when you are with your dad. Otherwise, the resentment or however you may feel doing something you do not want (or have the energy to do) will come through when you are with him. I am a firm believer in setting boundaries and taking care of one's self - in order to be present to support an other's needs. Otherwise, your health and well-being suffers. On another note, I realize many cannot afford to pay for certain care and are responsible to provide it - in this case, I encourage people to (1) get enough sleep; (2) eat healthy; (3) exercise; and (4) do some kind of meditation or spiritual inner work; and (5) incorporate some fun and down time in your schedule, even if just 30 minutes a day.

I am so glad Pam started this discussion. I have been struggling with dressing, bathing and toiling my mother since I moved her out of assisted living
(another story) and back in to her own home after 10 years. I have no siblings and have hired caregivers except for weekend evenings, where I've been doing the hands on for a year and resent it terribly. She's 96 and still very alert, but week. When I have to toilet her I just want to scream. I feel awful about it, but I just can't seem to help myself.
I appreciate all the responses and am glad to know it's not just me.....

I don't think many of us are particularly comfortable with carrying out personal care for our parents but what can you do? Needs must. Bowel movements are a law unto themselves and wait for no man or Carer.

I don't think that many of us are particularly comfortable with personal care for our parents but needs must. Bowel movements are a law unto themselves and wait for no man or allocated time when Carers come. Joy!

I completely understand. I went from retired and unbridled freedom, to moving out of my home, preparing every meal, 2 Dr. appts per week, while managing meds, yardcare, laundry, helping to dress, into and out of the shower, etc etc etc. After a UTI and a fall, and ending up back in rehab, Dad decided he would need help toileting when sent home from rehab. I asked weekly if he was handling it on his own yet. I proposed using tools like some of the little people had that couldn't reach back there, anything to enable him to do it himself so he could come home. When the answer was no, i told him I would not do that. The transition from helping him off the toilet, to cleaning him was a road I will not travel. I know my limitations, and we had reached them.

You can hire live in care giver first & then see how it goes

Someone should invent a self-cleaning wand with disposable pads, similar to the disposable toilet bowl cleaners you can now buy! Or install a bidet attachment to the present toilet to make the wiping easier.
I hope my husband never comes to that need. I physically gag and nearly throw up just by the odor.

I wish I had thought of, or someone had suggested the bidet option when we faced the situation. But having to wipe someone else rear doesn't come up in conversation too often, and I was reeling with the thought that he expected that I would do that. Not to receptive at that point.

I am the only daughter of my Mother. She has a son who lives on the other side of the continent. Mom has dementia. She lives in an assistive living facility. To take care of a mother as opposed to a father (male) is quite different for most people. I can understand your reluctance to "dress" your Dad and don't blame you for feeling bad about it. BUT, it is what it is and your feeling the way you do, as far as I'm concerned, is quite normal. I felt the same way about my Dad when he was in a nursing home and I had to help him do some of his very private needs. I also feel the same way about my Mom now with her dementia. If your Mom could afford it, I would certainly look into having the facility do the honors. Takes a load off, especially since you have your own life and also visit as often as you do. It's always easier for "others" to plant guilt just to alleviate theirs. I wish you luck.

Consider a "split"
Are you a morning person? Then maybe 4-5-6 days a week you go over in the morning and help him get ready for the day. Other days, paid assistance.
Or are you an evening person?
Go see him in the evening, maybe watch some TV or whatever you both enjoy, then help him into his PJ's and prepare for bed. Again 4-5-6 days a week, with paid help the other times.
It may sound easy to 'dress' him, BUT if you are not living in the same house with him, when you add in the travel time, parking, entering the building, going into his room, and the reverse when you leave, twice a day, it gets very involved. When you add in your travel time, etc, it is often more cost effective to have the dressing done by the in-house staff at the assisted living. Some elders are actually more comfortable with a 'professional' aide assisting them with dressing and showering than a family member. Consider his personal space and comfort level as well.
Wonderful that the family is working together. Sadly that is all too rare.

Pam I agree with all of the thoughtful comments above. This issue came up when dealing with my father-in-law. As an RN I was completely comfortable dealing with his toileting and bathing needs and, though not overjoyed at the prospect, my beloved husband was fine with helping me when necessary. His brother, however, was quite different. From the start we sat down to have a conversation about everyone's comfort levels. My brother-in-law was very clear on the fact that he would never touch his father, clean him or change him under any circumstances. We were fine with that and no judgements were passed as everyone has their own feelings and views on these issues. He felt that those tasks should be left to the professionals.
You need to sit down with your siblings, whether in person or via Skype or FaceTime to discuss your feelings about tending to the physical needs of your father. There is no shame in not wanting to do the tasks that you are opting out of. You should not allow anyone to make you feel guilty or less of a daughter for your choices. Given that there is money available there is a very easy solution. At the end of the day, it is likely that your father would not want you to feel obligated to do something that you were not comfortable doing. Try to remain calm in your discussions as you are going to need your siblings through Dad's illness.
Remember that we teach people how to treat us. Do not allow anyone, siblings or otherwise, to belittle you or question your character because of the choices you are making.
I wish you peace as you traverse the days and weeks to come.
Do not hesitate to return here if you are in need of any more support or ideas.
With gratitude and grace