As most have said, 4 is way too early to have an expectation of holding urine through the night. Most doctors won't even consider it something to start dealing with as an issue until age 6. It is usually genetically and biologically determined depending on the physiology of the individual. Children need to start producing the hormone Vasopressin -- which limits and slows production of urine at night. This hormone begins being produced by the body at different ages, and with it, bladder control at night. Until it kicks in -- there's nothing an individual can do.
Your child appears to have been potty trained at 2 -- which is remarkably early (most are not until 3). As pull-ups are effective, why not let your child develop as she was meant to, and reach her biological milestones when they arrive (you won't be able to rush puberty either -- nor would you most likely want to!). It seems you are equating her lack of control of her bladder (involuntary) with the "brat" tendencies you note she has. Brattiness at this age is normal too -- as a child is asserting her independence. So give your child (and yourself) a break. You've got a huge amount of responsibility with three kids -- but you are making it harder by having expectations that are unwarranted.
Here's some info from Familydoctor.com
Enuresis (Bed-Wetting)
What is enuresis?
Enuresis (say "en-yur-ee-sis") is the medical term for bed-wetting during sleep. Bed-wetting is fairly common and is often just a developmental stage. Bed-wetting is more common among boys than girls.
What causes bed-wetting?
Some of the causes of bed-wetting include the following:
* Genetic factors (it tends to run in families)
* Difficulties waking up from sleep
* Stress
* Slower than normal development of the central nervous system (which reduces the child's ability to stop the bladder from emptying at night)
* Hormonal factors (not enough antidiuretic hormone is produced, which is the hormone that slows urine production at night)
* Urinary tract infections
* Abnormalities in the urethral valves in boys or in the ureter in girls or boys
* Abnormalities in the spinal cord
* A small bladder
Bed-wetting is not a mental or behavior problem. It doesn't happen because the child is too lazy to get out of bed to go to the bathroom.
When do most children achieve bladder control?
Children achieve bladder control at different ages. By the age of 6 years, most children no longer urinate in their sleep. Bed-wetting up to the age of 6 is not unusual, even though it may be frustrating to parents. Treating a child for bed-wetting before the age of 6 is not usually necessary.