Another scenario re Agnes' parentage could be that she was the illegitimate daughter of Janet (Embroiderer) aged 26. It was not unusual in Scotland for a child born out of wedlock to have her father's name.
Also she could be the child of another daughter married to a Twaddle, who was not present on census night. She could be a widow, who was working away from her parents' home and they were looking after Agnes.
A Scottish family of my husband's raised three of their grandchildren. They were parents of the fathers. I don't know where the mothers went to, but the dads shot off overseas. (None of these were married).
Have you considered searching on Tweedale. I sort of think I have seen that as a variant of Twaddle. Will have a look at the census and see if I can find anyone who looks likely for the father.
Cheers,
MAGGIE