Yes, her thoughts were pretty unconvincing...but that's because she is convincing herself for something that is not right...but she vehemently wants it to be right. Padma saying, these kind of dialogues did puzzle me at first...
But she is defending Barkha so vehemently for a simple reason, and that is because she finds herself in Barkha. Padma being the 2nd wife of Harinath...sees her own reflection in Barkha...and Chaya's reflection (to an extent) in Rads...and hence she supports Barkha, come what may.
Yes, her lines did leave me aghast too. So she trusts Barkha who cured DDjee, sacrificed everything for the family etc. Padma is the same woman who once used to happily claim that "Radhika is the epitome of Sacrifice"...that Purohits can never forget the sacrifices Rads made for the sake of family...that they can never repay Rads for whatever she did for the family.
But now the same woman is supporting Barkha with the same lines. Reason? Perhaps because back then, Rads wanted Barkha to have everything and was leaving the house. But then things took a turn... and Barkha became the Rptian for the name sake purposes (this perhaps was the moment, when Padma started seeing her own reflection in Barkha...but it wasn't that strong) Padma continued supporting Rads sweetly...though she started having a special corner in her heart for Barkha. Remember she said, that once Dev is able declare Rads as RPtian, she would love to have Barkha as her own DIL (Rohan's wife) So Padma didn't want Barkha to leave the house, because she felt they have wronged Barkha (just like Padma was wronged without any fault of her's)
Her soft corner for Barkha started increasing...and then when Rads accused Barkha...this love for Barkha (or the strong urge to protect her own reflection) became too strong. When Rads went missing...and especially after Dev filled Barkha's mang for name sake purpose...Padma began seeing herself in Barkha entirely... afterall Barkha was being asked to sacrifice everything without any fault...so did Padma! Thus her soft corner for this girl.
But i guess, Kanha will let Barkha herself make Padma understand how she was supporting the wrong person always!