Meditation is basically a training method for your mind. When certain things happen to you, your mind generates a certain response whether it be happiness, frustration, anger ect. The way your mind has been inculcated is the path of least resistance and the path it wants to take, and will take unless you know how to mitigate it. Meditation teaches you how and makes it easier to override the process. Who is doing the overriding of this process? Well, that's the million dollar question. But I digress.
So here's what I'm getting at: if meditation is too easy, you're doing something wrong. You might be getting yourself really relaxed, but is it possible that's all you're doing? Not saying it is. I don't know, just throwing some ideas out there and it's up to you to see if any seem to fit your situation.
But as you meditate, your mind wants to grab onto the thoughts and not your breath. The course of least resistance is away from your breath and back into whatever thoughts are vying for your attention. Every time you go back to the breath, you train or teach yourself even, to take the opposite of the path of least resistance. This is coupled with the fact that half the time when you meditate, your mind says, "I'm tired. Stop concentrating on the breath and just kick back and let a guided meditation do most of the work." But every time this comes up you learn to drop it by returning to the breath and not listening to the thought no matter how loud and powerful it can get.
When you first start meditating you have this thought and then come back to the breath. But there's still a trace of this thought floating around in your mind and eventually it pulls you in again. As soon as you realize your back in that thought again, you turn your awareness back to the breath and away from the thought. But then it pulls you in again. And then you drop it again. You do this over and over and over. But as you practice you get better and better and faster and faster at recognizing it. You start to figure out how to do it most efficiently and quickly, seeing and dropping thoughts before they even become thoughts at all.
After doing this hour after hour, you gain a skill. One day you realize that you don't have to be sitting on a cushion to use this skill. I can't really explain how it's done, but it's just something you learn from continually focusing, coming back to, and holding your attention on the breath. It's like if you ever do a lot of push-ups, eventually you will realize, "I can flex my pecs." You couldn't flex them before, and you don't really know how you learned to do it, but now you can just do it.
So when I'm driving down the street and I get cut off, this magnetic, powerful idea pulls at my attention. But I've done this so many times before in my meditation sessions. It's not my first time at the rodeo. I know how to just drop it. I don't need to take that path of least resistance into anger because I have had so much practice choosing not to just take the path of least resistance and get pulled into the thoughts. That said, just because I'm better at dropping a thought process doesn't mean I always choose to. In fact, I still get irritated a lot, but not usually right after meditation.
I think it's more than just being better able to drop unhelpful thoughts. I think it stems form the fact that after you do this process with literally every thought you have and put hours and hours of practice in, your mind almost has this other mode where its immediate reaction is not to get pulled into the thought processes or emotions, but just to let it float by. This is how I feel after a meditation session. It's like my mind is so used to not letting ANY thought or emotion draw me in and start the thought process, that it takes a whole hell of a lot to produce an idea or thought magnetic enough to pull my mind into the old environmental trigger and thought process response mode.
This is why it's odd to me that after a meditation session, you feel like you let thoughts and emotions affect you more. You're mind should still at least semi-be in the letting thoughts and emotions go mindset.
Also, it sounds like you have a lot of stress in your life. Is there anything you can do about that? If I had that kind of stress, it would certainly be hard for me to get out of the thought process and have productive sessions. Not to say you can't. You definitely can, but it just makes it that much harder -- but also that much more rewarding when you can silence the stress.