When I am writing a very intense and dramatic scene, I often become overwhelmed by it and have to stop writing. Any tips on avoiding this and on focusing on writing.
Get everything that could be weighing on you outside of your story out of the way (do everything you must do for that day, settle things, etc.). Then, when you're in a good headspace, use that overwhelming feeling to your advantage to get neck-deep in the emotion. If writing it is causing you to feel things, then it probably is translating to readers and that's great so take advantage of it.
But if it's really overwhelming, like in a bad way, maybe just plan your writing carefully so you do it when you really know you are up to the task.
In two words, do not. It is perfectly fine to be overwhelmed. I laugh, cringe, and cry when I write, and then again when I read it out loud to my audiences. Sometimes I have to stop for minutes, because what I wrote or about to read is just too funny or sad. If you will try to rule your mind with an iron fist, you risk losing your inner self that makes you a writer.
PS: This should be considered one of the best questions on WSE.