My DS refused to poo. His was caused through trauma from chronic constipation issues.

Are you certain that she is not still undergoing the constipation cycle? Just going from your post, she should from my understanding (no matter how many poos she is doing) be doing a 3-4 on the bristol stool chart, so that is sausages without any hard lumps, no struggling to pass, no pain. The fact that you are using movicol occasionally suggests to me (and Im no doctor and my definitely be bias towards constipation lol!) that she is not past the constipation cycle. If you have prolonged unresolved constipation then it becomes hard for them to recognise the need to go all the time until the body is pushing it out against her knowledge.

Something you can try is the books to normalise pooing. We have three different ones, wheres the poo, everybody poos and another one I cant think of from the top of my head. My other suggestion is to modify your toilet routine. DO NOT mention poo, just put her on the toilet after every meal, for 5 minutes at least. Give her a rewards for sitting and then another if she poos. We used this method with DS and within days he moved past toileting refusal! Might be worth another shot. Consistency is the key also. Good luck.