From what I saw in Asunder and TME I have a hard time believing that Justinia has that much influence.
She clearly did have enough influence to be named and elected to the Divine herself. That is nothing trivial in itself because the position itself is very valuable (though you have to maintain it to get anything out of it). That suggests allies among the Grand Clerics (I'd guess that Elthina was one of them), though it's unlikely she had the complete support of all of them. After all, if she did why was her being named questioned at all.
Moreover, we now know she has the ear of empress Celene. So we're not talking about someone non-influential here.
But... there's no such thing as absolute power. Justinia V has been elected on equally much negotiation as influence and blackmail. She has expectations on her to fulfill certain things, not do certain others and uphold this or that value. If her supporters come to the conclusion that she will no longer do what they expect of her, she'll lose their support. Without their support, she'll lose the ability to do what she wants and needs and without the abiltiy to do what she needs she'll lose more support.
So she has to balance the expectations on her with her own ambitions.
This is why she couldn't say... get rid of Lambert. Because the loyalty of assets and allies hinged on her not starting to removing people in position of power because they displeased her.
Similarily, she may have wanted to deal with the mage-templar conflict on her own and at her own pace, but the threat it presented against Orlesian interests made it a matter the imperial court needed resolved sooner than she would have liked. But in both cases you simply have to adapt or accept the loss of power.
But all people in power faces considerations like these. You don't even come close to power without having a deal of competence in dealing with matters like these. That you're not always in complete control does not mean you're not influential or powerful. Your ability to seize back the initiative is a far more important trait.
There'll always be one crisis or another that will destabilize your position and you will not always chose the correct cause of action either. That is life. Seeing such things happen is in no way indicative that someone is a poor leader or does not have influence.