Hi J S - I can imagine that is really frustrating for you. I encourage you to back off just a little just so that she doesnt start controlling the situation by refusing to go potty, etc. Resistance to going or just not wanting to stop what she is doing in order to go potty is pretty common and very well could have contributed to her initial constipation.
I would encourage you to pick one or two times during the day like after breakfast or as part of the bedtime routine to have her sit on the potty to have a b.m. At first she may be resistant to sitting there long enough to go so perhaps she could take a toy or a book or you might need to sit with her a read, etc. It's gross but at first that will help her relax. She may also need some coaching. 10 minutes is a good starting point at first. If she isnt successful in the morning, try again at bedtime. When you find a time that she is consistently able to produce a b.m. then she will probably have better success keeping her underwear clean, although some breakthrough is to be expected.
edit: JS - thought I would let you know that my 6yo contributed to the advice in this message. : )
Good luck!