Is she just two, or two going on three? There’s a big difference, but in either case only a day or two of potty training is way too soon to expect much at all in the way of results.
My daughter was two months away from her third birthday when we switched to underwear. She’d been introduced to the potty long before then, of course, and knew the routine. She could pull her pants up and down and communicate very well. However, she had no interest in wearing underwear all of the time. Since she was in daycare, I chose the week I had off work for Christmas to get rid of the diapers. It really helped to be with her all day and not put the job off on teachers who are also responsible for several other children.
First, I set a timer to go off every hour. When the timer went off, it was potty time. We’d go into the bathroom and she’d sit on the potty. If she went pee or poop, she got an M&M candy. If she didn’t do anything, I’d remind her to keep her pants clean and dry and we’d wait a while to try again later. The first two days she had one or two accidents. The third day, it all went to hell. She decided she was done using the potty forever, and would sit on it until she had a ring around her bottom (refusing to get off) without going pee. As soon as she finally stood up and pulled her pants up, she’d pee. Then, she’d laugh. I was so frustrated and didn’t know what to do. It was clearly a battle of wills. After this happened several times, I was ready to give up and wait.
Then, a friend of mine gave me some excellent advice. She said, “When she wets herself, make her clean herself up. She’ll hate it so much, she’ll keep herself dry.” I first explained to my daughter, “You’re a big girl now, and you wear underwear. It’s your job to keep your underwear clean and dry. If you pee in your pants, you will clean it up.” So, the next time my daughter sat on the toilet for 45 minutes, didn’t do anything, but immediately peed in her pants, I calmly took her into the bathroom and told her to take her clothes off and put them in the hamper. She was horrified and completely disgusted. She didn’t want to touch her wet clothes, and cried and cried. I stayed calm, but insisted she do it herself. She finally pulled off her wet clothes and put them in the hamper. I helped her put on dry things, but she was still furious with me. She was so mad she said, “Mommy, I am going to bed!” and spent almost an hour in bed being angry before getting up again.
It was the last time she had a wet accident during the day. She did wear pull-ups at night until she was able to stay dry, about another year. Typically when a child has kept the pull-up dry for three nights, he or she doesn’t need it any more. My daughter never kept it dry, but once we stopped using it, she didn’t have any accidents. However, please keep in mind that it is very common for children to take a lot longer to have bladder control all night, especially boys. It is not laziness. Some children’s brains do not signal the kidneys to slow urine production during sleep, and if these children are also very deep sleepers they simply will not wake up to use the bathroom. It takes time and patience for them to mature.
As for pooping, it’s sometimes different for kids to learn to poo on the potty compared to learning to pee. Even after our daughter stopped peeing in her pants, she had a couple of bowel movement accidents. She had been constipated and was afraid to poop on the potty because she thought it would hurt. It took another couple of days of rewarding her for pooping on the potty and being very patient for her to go to the bathroom when she needed to have a bowel movement.
Potty training my two boys was similar, but they were a bit older.
There are many, many resources for parents starting to potty train. Visit the library or book store, look up articles on the internet. Use the method or advice that fits best with your family, and above all, be patient!
Edited to add: I did not try to make my child clean herself up if she had a bowel movement in her underwear. That’s too nasty. We simply bribed her with candy and small toys until she got over her fear.