Mother enters, being one who refuses to admit to going back but stayed (8)
I believe the answer is:
remained
'stayed' is the definition.
('remain' can be a synonym of 'stay')
'mother enters being one who refuses' is the wordplay.
'mother' becomes 'ma' (Ma is another word for mother or mum).
'enters' indicates putting letters inside.
'being one who refuses' becomes 'reined' (I can't justify this - if you can you should believe this answer much more).
'ma' inserted inside 'reined' is 'REMAINED'.
'to admit to going back but' is the link.
This may not be correct. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for remained that I've seen before include "Stayed behind" , "Stayed put as I meander" , "didn't move" , "Was left" .)