@mVitus
Well, you’ve opened a whole can of worms and there’s a ton that could be said about this. My reply will only scratch the surface.
If judgmental and/or agitated feelings are coming to you, I’d say you’re definitely on the right track. This is a good sign and it even demonstrates a maturity in conscience and you shouldn’t be surprised by it. There is suppose to be some resistance. That’s how athletic training works and spiritual training isn’t all that different.
Our spirit longs for God and godly things, but our human nature withdraws from it and wants to be evil. Doing the right thing is always about our will, never our feelings or our mood. So your feelings might tell you how so and so did such and such, and if a person hurt you in the past some of those feelings might boil up inside either a little or a lot, but you can still will for their conversion, salvation, and eternal happiness. St Thomas Aquinas says that loving is to will the good of the other. Also, remember that conversion is a lifelong struggle of getting closer to God, and it’s something we all pray for and not just for the so-called great sinners.
It is also helpful to reflect on your own sinfulness and inadequacy before beginning your prayers for other people. This is something I do and it’s strongly recommended, especially in Ignatian spirituality. Also, I think about all of the advantages or benefits I’ve been given that I haven’t earned: a healthy body, a healthy mind, my material benefits, my support networks growing up, my academic & spiritual education, etc., and then I reflect on where I would be if I had none of those things. Think about how much more weak I would be, or how ignorant, or how confused/lost. How utterly incapable I’d be without God supporting me every day and every second. Once we do this, it can soften our view towards others and incline us towards compassion.
Peace.
(If you don’t mind me throwing a book suggestion at you, I think St Alphonsus Liguori’s “A Short Treatise on Prayer” might be very helpful for you. It was for me. Bear in mind it’s an 18th century book so the language is a little thick sometimes, and he is a man of his time and culture just like anybody, but over 95% of it still applies today.)