Honestly i dont find any fault in archana's challenge. Agree she is behaving very weirdly with arjun and not even giving chance to him to explain his story but she has her own reason to behave like this. Arjun was not able to handle everything properly and result he spoiled his image in front of archana otherwise archana was impressed with him coz he is son of DK and Ashna.
We as a viewer know about intention of arjun but after creating such a big fiasco i guess arjun is not less than any play boy for archana. If she literally wish to seperate arvi than she should have asked arjun just to leave. Bt she is ready to give another chance to arjun. But if this time she wish that arjun should prove his love than what is wrong in it? Coz she already has 1 bitter experience of arjun so this time he has to struggle. So i guess challange is not big deal...