I think for the self doubt, you can tell them you have some doubts. However, realize that they want to be with you. So if you worried you are butting in, then tell them that they must tell you if they want to do something just between the two of them. That way, when they don't say they want that time for just them, it means they want to be with you. For that to work, they have to feel comfortable saying it and you have to handle it well. But in the end, you will know that the time you have with them is time they want with you.
Temper is a tough one. You have to learn the art of having the feeling but directing it from being self destructive. This is very individualistic. Many ways of dealing with it is to take a little break and let the hormones settle down some. Talk a little walk or count to ten.
Also try to be aware if you are using anger to hide other emotions like wanting to cry or feeling vunerable.
I wish you well.