Hi and welcome! Usually it is suggested to leave them to settle in to their new home for at least a week before you start gradually handling them. You've only had her for a couple of weeks so I wonder whether she has not had this time to settle in. She may have been through a bit of an ordeal before she went home with you (especially as she is likely a wild import).
I suggest shortening the time you have her out with you - keep it to about 10 minutes at a time. Pick her up making sure you support her body so she feels secure (see
Here). Hold her secure and let her sit on your hands but don't 'pet' her, if you know what I mean, don't stroke her. Then after a short time put her back in her enclosure. You are trying to change the pattern so that she can be out with you and back in without too high stress.
You can try to feel her occasional treats as well by hand either while she is out or in the enclosure (see the
Diet chart). That is a common way to build trust too. Although admittedly it didn't work for my skink personally as she refused to eat anything from us unless we plopped it in the security of her enclosure and left her alone.
They don't really need to 'pee' as such, they usually get rid of extra in the urates (white stuff) with poo but will do an occasional wee, especially if stressed out.
Anyway, just my suggestion.
This is a good read too about what to expect with a new skink and
another on taming. Let us know how things go. Also keep an eye out and make sure she is eating well and maintaining good weight to rule out an internal parasite issue.