i had the same problem at that age. in my case going to the toilet triggered a lot of anxiety and i use to wee in my pants so i didnt have to use the toilet. in my case there were also a lot of other contributing factors. i started weeing in my pants at 4 as well not long after my father started handling me sexually. i was toilet avoidant (unless at school) until 12 - i matured out of it myself, eventually.
sorry its not an answer, just another avenue ?
Being that she has been doing this since she was 4, she must have some condition with her bladder that the doctors are missing. Does she hold it for prolong periods of time? Does she get bladder infections? She may just have a relaxed bladder. She may need to be taught on to hold her urine. When she does urinate, does she go a lot or just a little? Sometimes kids go just a little and never get the bladder control that they should have. They do need to hold it to develop bladder control. On the other hand, some kids hold it a long time, too long, and then oops.
Sounds like overkill, perhaps she is anxious thats why she is doing it, doesnt sound as if punishment is a good idea will only re-enforce the concern she has, Perhaps take a step back .make it less of an issue ,pullups&pads at her age are a punishment it will make things worse, perhaps she is missing her bio mom as she is with you each day ,how many days and nights is she with you maybe her Mom should keep her with her more.as there isnt an issue there.