Just wanted to tell you your three-year-old is well within the range of normal. If family members are suggesting otherwise, laugh it off or change the subject, and remind them how important it is for everyone in your family to get a good night's sleep.
You question struck a chord with me because last summer, my family puchased a Malem bedwetting alarm and we finally conquered my seven-year-old's nighttime wetting completely. I have read quite a bit about bedwetting as we struggled with wet sheets and discouragement, and I can tell you for sure it won't last forever, and it's not until after age 5 or even 6 that most pediatricians will suggest intervention (such as an alarm). Your daughter sounds healthy and normal.
The best book I read was called "Seven Steps to Nighttime Dryness." I highly recommend it if you're feeling frustrated. I got it with the alarm and a couple of sheet overlays (such lifesavers, since you don't have to pull sheets off and re-make the bed in the middle of the night) from www.bedwettingstore.com, although I'm sure you could find it on Amazon. The progress chart in that book was immensely helpful.
You're dealing with primary enuresis (wets during sleep, has never been dry). This is developmentally normal. Secondary enuresis (was dry, suddenly wetting during sleep) is the red flag for a problem such as urinary tract or kidney infections.
Our pediatrician advised against limiting fluids--for primary enuresis it's not likely to make a big difference and being dehydrated is not the same as being continent, you know? Some children are more likely to stay dry when they avoid soda or dairy products. Also, some primary enuresis is caused by constipation--the theory is that an overfull colon presses and rubs against the bladder, desensitizing the child to the urge to urinate. (Usually you'd notice other symptoms, such as encompresis or stomach cramps, if this were the case.)
One thing that is very useful is double- or even triple-voiding before bed. Urinating at least twice right before bed (like, before and after you brush her teeth) can help the bladder get completely empty so there's not an immediate urine release while sleeping. Leaning forward slightly on the toilet also encourages complete bladder emptying.
My second son slept with a Pull-up until he was nearly 4, but gradually became drier and drier until he was dry overnight and would rush to the toilet in the morning like the rest of us. He did this on his own as his body matured and we offered no coercion or comment except to have him take care of the used Pull-up and cheer with him when the Pull-ups were dry.
With my two vastly different experiences, I can say for sure there is much value in keeping nighttime dryness issues from becoming an emotional stressor in your family. Children need good sleep to grow and be healthy and happy. If they feel responsible for "performing" a task while they sleep--one they are not even conscious of--then bedtime becomes stressful and loses the peaceful, reassuring tone it should have. You can experiment without using a Pull-up, but it is not like daytime toileting, and I suggest you avoid a "do or die" attitude. If she's not dry, then revert to Pull-ups until there's some consistent dryness and then experiment again. Waiting for developmental readiness is not the same as enabling laziness!
My sincerest best wishes to you and your family! :)