I'm with you on the trinity, but I think I separate them in my mind. i.e. God (my father), Jesus (my savior and helper), and the Holy Spirit (the one who indwells, and teaches and directs me). There is a lot of overlap for me, so well, that's my general idea of how it all hangs together.
Like you, I have had experiences in my church where I knew God was present. It's always was kind of electric and all-encompassing for me, and very deeply felt. One time, we were singing "Whom Shall I Fear" with the band/choir when the band stopped playing and all of us were singing a capella. I, too, had tears running down my face. I still get shivers when I think about it and I feel deeply moved. Going to church is usually very emotional for me. The music touches me on a very deep level.
I go to a really big church and there all kinds of hands raised and singing as we have a great band, but no speaking in tongues or anything of that nature. If I were to give it a label, it seems to me we're all kind of Charismatic meets Methodist of a sort at my church. :) Some fall toward Calvinism, others are more liberal. I tend to not get hung up on religious semantics, but instead focus on my relationship with Christ, so I guess I'm just a believer without a label.
I have had many experiences with God as well. I had one the other day when I went to Walmart. A lady approached me from behind and asked if I was a Christian. Hmmm, I was talking to God when she approached, asking Him to help me through this horrible apartment move I have going on. So, I said "yes" and she told me that He wanted me to know that He loved me deeply." It was a bit shocking, but I think it was Heaven sent. We both looked at each other a little stunned and then hugged.
Not sure this is what you're looking for, but it's how I experience God daily on every level of my life. I hope someone else can add more to this for you if I'm off track. VB