Yes you can. You request a full report, or I believe you can request single conversations only. In Colorado these are self authenticating and can be used in court as exhibits.
If You typed out the messages originally on either your phone or your computer then unless you erased it you have the original copy You don't need a copy from nobody else You have it you typed it.
If there's a court order that you use the app and the other party does not comply, it can be a contempt issue. However, the app is not for your communication with your children, and the years of no communication indicate a bigger problem. I suggest you speak with an attorney in your area.