Catherine did not admit to Henry or to anyone that she lay with Arthur and maintained that until she died.
Catherine did not voluntarily leave the palace. She was forced to by Henry. She said "God never called me to a nunnery. I am the Kings true and legitimate wife."
Henry asks Thomas Boleyn to have his daughters at court right before Catherine leaves. Anne and Mary Boleyn were at court for several years before. Mary Boleyn even had an affair with and possibly two children by Henry before Catherine left.
The ending makes it seem that Catherine was able to take Mary with her when she left. By the time Catherine left Mary was already living in Ludlow Castle and after the separation Henry would not let the two see each other again.