My dd had caps placed on her top four front teeth when she was 2 years 3 months, in the dentist's office with an oral sedative (antihistamine) and a papoose to hold her. So here's my advice to you....
Now that I have so much more knowledge about different approaches and the different options available, I would have asked to wrap her in her own blanket and hold her hands myself. The papoose was too confining. What bothered her most though was the numbing feeling after the local anesthesia shot. She started crying then and cryed pretty much the entire hour. When she was 4, she sat through a shot and small filling with no problem whatsoever, just holding my hands. She closed her eyes and I thought she was asleep because she was so still. But she told me later that she just didn't think about anything! She totally trusts her dentist, loves his corny jokes and feels like a very brave girl when she's done.
I avoided GA because I personally was not comfortable with it. And the trauma of her first experience did fade and now she knows how to breath through any fear that comes up. We talked a LOT about getting through the treatment.
Because your dd is 3, she is at the age of reason. She will most likely be able to listen and comprehend more what's happening than a young 2 year old. If you have any doubts about the GA, and you think your dd's temperment can handle the time in the chair, I would talk with the dentist about other options. Dd's 4 caps took about 1 hour. You could also talk to your dentist about doing it in a couple of sittings.
In retrospect, I would have chosen to wrap dd in her blanket and given her nitrous oxide. NOT the oral sedative. Nitrous is there when you have the mask on, gone when it's off. The oral sedative stays in her system. It was weird to see dd so out of it when I first gave it to her. (an hour before the appt.) But by the time she was in the chair, it seemed to have no effect. There are also essential oils you can use for calming, hypnotherapy which sometimes is just the rhythm of the voice, and accupressure as options.
Now, the problem we encountered was this.....dd's two middle teeth abscessed 5 months after the caps were put in place. So I always questioned whether the decay was advanced enough that these two teeth had warranted a pulpectomy (is that it? I get pulpotomy and pulpectomy mixed) anyway the "baby root canal", before capping.
I was fearful of the infection getting serious, so we had those two teeth extracted, and now she has two false teeth in place until her adult teeth grow in.
It is my understanding that the decay in baby teeth affect the adult teeth if left untreated. The decay can lead to infection which then affects the adult teeth.
I don't think children have the same issues with ill fitting caps as adults. I am sure your dd will let you know if there is discomfort. Dd has never complained about her caps or her false teeth bracket.
How advanced is her decay? I have read some stories here where a dentist will do multiple treatments of scraping to remove the "crud" and paint on flouride to strengthen and remineralize the enamel instead of the capping. Capping can be both, necessary if the tooth structure is so far gone and the decay too far advanced, but it can also be the "easy band-aid" if the dentist doesn't want to spend the time and energy to deal with the decay.
Have you considered getting a second opinion from another dentist?
I hope this helps in your journey