Another route is to learn to look at the relative "importance" of whatever is wrong?
My T worked to teach me that "a wet towel on the bed is not a murder"

I lumped all negatives into the same, intense category.
When you are going to a party, yes it is disappointing to be late and relying on someone else to drive who is inconsiderate (doesn't call/warn you they will be late) and late would be frustrating and I would feel angry toward that person but there are always actions one can take to work on the situation instead of just trying to "lessen" the emotions that are informing you that something is wrong (think how pain informs you there's a problem with your body).
Did you call the person who was late, see what was keeping them, how late they'd be (knowing when they were coming might make you feel better instead of the unknown scheduling/lateness factor)? Did you wait X minutes and then just drive yourself, leave a message on the late person's phone not to bother to pick you up, you'd drive yourself; you had decided you would rather enjoy the party than drink too much?
How we feel is all about us! It's information our body is giving us about how we're doing with ourselves, others, and the situation surrounding us. The feelings are always "right" because they are ours! Our perceptions can be wrong, that's why we have to check out what we are
thinking with any others involved, but our feelings can never be wrong.
When we have an feeling, we have to figure out how to respond. Self-soothing intense feelings is a form of suppression of the feeling. If I told you a tornado was coming in 10 minutes, you wouldn't say, "that's okay, it will be okay; it might be scary but I can handle that" you would do something, would take cover or leave that area or find out additional information to see how bad it was going to be.
When someone is late, the first thing is to decide how late you are going to allow them to be, how much personal unhappiness/emotional "pain" you are going to allow yourself to tolerate? When you have a headache, how bad does it have to be before you take an aspirin? That's exactly the same sort of thing you should be thinking when you have an emotional problem.
So, you decide they can be 10 minutes late and you can tolerate it. When they are later than that you have to go to the next step and decide your options. Do you call them or do you find another way to get to where you are going or do you decide the trip isn't that interesting/important to you and go back inside and back to whatever else you were doing or do you decide to wait "just 5 more minutes" before considering your options again?
A good next step is to call the person who is late; not just because they're inconveniencing you but because they may be in trouble or have forgotten they are supposed to pick you up. You are always responsible for getting you to the party, because someone else offers and you accept, doesn't mean you hand over the reins to your life events! You are going to the party. Other people may be going too but they are not you and are not responsible for you.
You soothed yourself partly by blaming the other person for messing up your plans; other people can't mess up our lives; events may change our plans but they are always our plans and we are responsible for making them so they work for us. If something doesn't work for us, we have to try something else that does.
Being active in our lives, responding positively to our emotions, is the only way to get where we ultimately want to go, to move forward in our own lives.
But the first alternate choice I offered, "a wet towel on the bed is not a murder". You can re-evaluate the situation and scale down your reactions toward it. It's just a birthday party. It's a fun thing, whether I'm there for 30 minutes or 3 hours, that time will be fun. I don't like to wait but if I call and find out how long the wait will be I can use that time, not to "wait" but to do something else I want to. I can "turn off" that I'm going to be picked up at 1:00 and know I don't have to be ready to go until 2:30 now or I can learn my friend doesn't feel like taking me after all and decide not to ask them to take me to an event where getting there on time is important to me in the future. I call another friend or drive myself or don't go (after calling my host/ess to tell them I can't make it, my ride fell through and I'm so sorry but hope the birthday person and I can get together real soon) or find, from calling my host/ess that someone will be right over to pick me up, they wouldn't dream of having a party without me
If I feel my feelings are intense, I have to look at the event (a party) and notice that the intensity looks a little "odd" and what else might be going on? Darn! I wanted to have extra to drink and now I'll only have 30 minutes to drink instead of 3 hours! If that's the case, it's not getting to the party, it's the drinking I want (being honest with one's self goes a long way at understanding one's emotions which are always honest with us) and I can then figure out how I can drink at home/now or work on my drinking problem which I'm allowing to influence my life too much (such that I feel so intensely about being late to the party not because I really want to go to the party but because I'm being thwarted in my drinking).
Working with our emotions can be a lot of fun because they are so interesting and complicated! They are only ours, too, something of us! They are like a treasure map to our lives, showing us the directions we need to go to move further along our "path".