Do We Not Believe God Is With People?

"God, please be with...." 

I can't be the only person to have prayed a prayer with these four words. Nighttime, when I'm trying to fall asleep, is when I do my deep thinking (apparently). I had been praying and then I said those four words, "God, please be with...", and I stopped. Why do I say that? Does me praying, asking God to be with a person or situation, reveal a lack of trust? 

As Christians, we say we believe that God is omnipresent - present everywhere, all the time. Why then, would we ask God to be with someone? We already believe He is there, right? We needn't ask Him to be somewhere He already is. What then, are we asking?

I know what I really mean - or what I think I really mean - when I say "please be with...". I'm asking that God help the person with their situation; that they would feel His presence and peace with them. Or maybe I'm asking God to work in a certain situation. At least on a conscience level, I'm not doubting that God is there.

But here's my question: do the words with which we pray reveal something about our beliefs? Maybe I'm just quibbling about semantics, but if our words reveal our deep beliefs, the ones that we might not be consciously aware we hold, then shouldn't we be paying attention to the words we say when we pray?

If I say I believe that God is everywhere at all times, but pray as if He's not, then I have a problem. Now that I'm aware that I say "please be with...", I'm trying to not say those words and instead say what I'm actually asking for. "Please help them" or "let them feel Your presence and peace". 

What do you think? Am I making a big deal out of nothing, or not? Let me know in the comments (or if you know me, we can talk in person), because I certainly don't have an answer and you can only learn so much thinking about things in your own head, as interesting as that can be ;)