Hello Sadegirl,
Wow, I recognize myself in so much of what you wrote.
I have been diagnosed with RAD about a year ago. I have taken a Mindfulness course and I've had regular psychotherapy (so not specific to RAD) and as to your question: Yes! Thankfully you can improve and there is no need to just resort to modifying behavior and pretending.
Most of my life I've lived adapting to other people and as a result I've pushed away everything that was *me*. My emotions, wishes, dreams, needs, etc. I would feel shallow emotions, but lately I've found out that those shallow emotions are just masks that keep me from dealing with the deep and heavy emotions underneath: misunderstanding, rejection, unwantedness, feeling unsafe, feeling that I don't really have a right to walk on this earth if I am not perfect. I SO understand what you're saying about being afraid of being honest about your emotions. All due respect to TiaFierra, but I disagree with her about "I can't be honest being an excuse".
RAD is a disorder that often leads you to fight against either yourself or the world around you. Reading your story makes me think that both of us tend to fight against ourselves. Because of the RAD I believed that I was worthless, unwanted and unloved if I'm just the way I am, and that the best solution is to "become someone else". I fought against myself, pushing away everything that was *me* and forcing myself into the mold of everyone I came into contact with just so I could be liked.
Forcing yourself to be someone you're not is not the solution.
For instance: I used to lie a lot so people wouldn't see "my true horrible real self" (as I saw myself). I hated the lies, and hated myself because of the lies. I tried to tell myself to stop telling lies, but because I was so scared of people disliking me I couldn't help myself and would hate myself even more. However: now that I can accept that I have a social problem, I can protect myself in other, healthier ways and the need to tell lies is gone.
Instead of forcing yourself to become different (and actually worsen your frustration!), I think you should find a therapist that can help you get to the root of your problem. That can help you get in contact with your emotions and help you deal with them instead of going back into your automatic respons of "supressing".
Someone that can also teach you to recognize and acknowledge your emotions and teach you to gently tend to them. As you are learning to accept who you are (incl RAD) and effective support yourself, there is no need to force yourself anymore. Instead of forcing yourself to stay in a relationship you can learn to think this way: "how can I support myself so I can feel safe in this relationship again?" or "Can I allow myself room to grow?".
To a degree symtoms will fall away, or become less frustrating, as you learn to accept who you are and be patient towards yourself.
That's what I learned from therapy and it lifted a huge burden off of my shoulders. I am much more at peace with myself, much happier and much better equipped to deal with things that come my way.
My RAD isn't gone. Relationships will probably always be more difficult for me than for most people, but I don't need to pretend or push myself anymore. I can accept myself and look for useful and healthy solutions. It's a HUGE relief.
About your fear of not being honest to a therapist: I was very afraid of telling her my deep emotions (which is normal with RAD), but I learned to not expect myself to perfect immediately. Trust is a thing that grows and needs time. So, entrust your therapist with small things first and slowly stretch that a little as you gain a little more trust.
I never told my therapist everything and I didn't need to. Yet she helped me grow tremendously.
A good therapist should know that trust needs to grow, and respect your choices regarding what you are and aren't comfortable saying. But like I said earlier: Don't force yourself to "just do it", that's just gonna make it worse. Be patient with yourself.
Oh and: I would definitely advice mindfulness btw! It helps you to get into contact with yourself again and worked wonders for me. I discovered parts of myself that never even new existed!
Just be sure to find someone that doesn't give mindfulness with a very religious background, but one with more of a medical background.
And combine it with other therapy. In my experience mindfulness can bring up many emotions and it seems that you (like me) have one automatic respond: supression. So also find a place where you can learn to deal with the emotions that you might discover during the sessions, otherwise you might just flip back-and-forth between "finding emotions" and "supressing".
I'm sorry it's such a long post. I don't know how I explain what I've learned in a short post

I hope this is helpful though