Not sure I have any answers but yes I can relate to what you describe. I don't have DID but I'm very introverted and have spent a lot of my life living inside my head. As a result, spirituality has become very important to me, particularly in recent years, and I've had a lot of experiences. Around two years ago I started a new relationship and one of the things that worried me was losing touch with my spirituality since I was obviously more focussed on the outside world. I didn't have to wonder long because the relationship ended after 8 months and it was mainly long distance. I do wonder how I'd cope if I were living with someone and how it would affect my relationship with my spirituality.
I know that some deeply religious and spiritual people find a way of sharing their spirituality with the world/close relationships. But others want to be alone. It is said that the spiritual journey is a lonely one by definition because it involves turning inward and searching your own soul. But I don't believe it HAS to be done all alone. Relationships are where we learn the most about ourselves anyway. I think it's probably harder for people who grew up alone as children to find a balance as the tendency is to cut off from people.
You can be calm and in the world. Meditation will help if that's your kind of thing. It doesn't have to be lotus position and mantras...there are plenty of modern ways to do it and it will help centre you so that you don't lose touch with your inner self while with others. Perhaps the fear is losing yourself because in childhood you couldn't define your boundaries...but as an adult you can, it's possible to get to know yourself and share yourself with the world without fearing the loss of you. Daily meditation might help you connect to yourself and your heart centre as well as give you the space you need for yourself so that you remain aware of who you are. Rambling but hope this is some help.