I started potty training similarly, asking my daughter if she wanted to use it. The answer was always NO. At about 2-1/2, we got to the point where she was holding it so long that the flood when she actually went would leak out of anything except a doubled cloth diaper, which didn't fit under her clothes...So we decided it was time to potty train...It was a painful for us, but it worked.
First, I cleared EVERYTHING from our schedules for the week. No errands. No visitors. No distractions.
Second, I told her for several days that she was going to get to wear big-girl panties (no waterproofing). After that, no more diapers during the day. I dressed her in the panties and a shirt to cut down on laundry.
She resisted. We went a full week of my setting the timer to let her know when to try. She would hold it until she couldn't anymore and go wherever she was standing. I would clean up the puddles and we would start again.
We eventually had a couple of happy accidents. After bath, she wasn't dressed yet and ran to the potty to go by herself. The next morning, I was cleaning up after an accident and hadn't dressed her yet. She went potty all by herself again.
In the end, she spent about two days naked from the waist down and immediately had no accidents at all. But she chose to use the big potty rather than the potty chair, even figuring out how to climb onto it by herself.
After a week or two, she started wearing pull-ups or waterproof training pants when we left the house. Now we're down to needing them only for night.
Some other things we tried that seemed to help (although I think she just made up her mind to do it herself...):
-Her favorite stuffed animals used the potty before she tried. Make sound effects, wipe, pretend to flush, etc.
-Rewards--We used chocolate chips for going. When she had full days without accidents, she could choose a potty prize (I had a little box of dollar store toys).
-LOTS and LOTS of PRAISE
As far as wiping goes, I use TP for wet. When I wipe, she leans forward on the potty so I can reach her. I bought flushable toddler wipes for poo after having trouble getting her clean.