I have been with my partner for almost 9 years, and although we were never married, we were engaged. My ex walked out on me and my 1 year old son, with no warning, and then sought legal advice to try to get residence of him. By luck, I managed to keep resedence, until we finally decided to sort things out ourselves. We got back together, and 18 months on, we now have a second child. Two days ago, she walked out again, this time taking both of our children with her. I am deeply concerned about the welfare of our children, as the oldest, who is now almost 4, has been a different child since she first abandoned him. I have been a constant source of stability for both of our kids, but especially for the eldest, as he has been through this before. Is there any way I can obtain a residence order, or a shared residence order, as at the moment, I am not allowed contact, and messages I send my ex are completely ignored, even though they are purely for our children. I have parental responsibility, as both children were born after April 2003, and I am on both birth certificates. Any help or advice you can offer will be greatly appreciated.

Not sure where you are at, since you are not using the term custody I will assume not the US.

So I can only talk about the general US law ( which differers some from state to state)
You willl need an attorney and file court papers ASAP asking for what you want and trying to get a hearing ASAP.