Happiest, first I would like to send you a huge bear hug because everyone can use a hug everyday especially when they are hurting inside. Second, when you are angry at someone it is very difficult to show compassion towards them or serve them with the same focus, attention and energy than when you are on good terms with them. Davening would fall into that category. We are obligated to show hakaros hatov and to daven to Hashem, so if you do it grudgingly, obvious it would be a very difficult task or it would be done completely without meaning.
I am wondering if the words of Tehillim would be a nechama for you. Some times when I am feeling angry and frustrated instead of davening I turn to Tehillim to feel better because it expresses such a huge array of feelings and emotions. No matter which kapitel you turn to, you can correlate something in there to something that is going on with you or at the very least an emotion you are in touch with. And obviously it is possible that the tears will flow, but that is fine. At times I read the words of my Tehillim right through the anger and the tears until I felt better, validated and reassured.
When you daven the same teffilos everyday, I don’t believe we always pay attention or really understand the words. On the other hand when we pick up a Tehilllim we usually say it with such Kavonah, as if we want to rip an answer from its pages or we are begging for an immediate result.
That is how I feel and the difference for me. Is it possible that you feel differently about Tehillim and that you can try to say some Tehillim just to soothe your own inner turmoil?