For Mohini chachi,it is to prove that she is the boss and everyone in the house should listen to her.
she suspects Paro and want to convince herself that she is not what she claims to be-rudra's fiance.
so she is putting her to the test agnipareeksha😉😉
Good that R said no.
then Mohini got upset,since noone in the family disobeyed her at any cost,so the only asthra that she had used on him---his mother...
For Rudra---paro is noone to him,so legally or otherwise,she does not have any right to touch his shoes.that is why he said no
For Paro,uncertain future,volatile household, she is hesitant ,ususre of what to do,in the end does as the mistress of the house says...