Neither can "throw" the other out of the house. In Virginia, however, you still are legally married and adultery still is a crime so your "dating" could be a criminal offense and certainly grounds for divorce. Since the two of you are living like this anyway, it would seem prudent to discuss the terms of an uncontested divorce and the legal dissolution of the marriage.
If the Order was never entered then there is no Order. If it was "presented", but not "entered" and it is in Virginia Beach where Orders are routinely rejected for various perceived problems, it is likely that there was some issue with the Order that needed to be corrected before the judge would enter it. You can go to the Clerk's Office and review the file. A phone call will not tell you much.
If there is no custody order in effect, then you legally are able to go get her. Whether that will have a positive or a negative effect will depend on all of the circumstances and the judge who hears the case.
As with all child custody matters, you and the father should make every effort to resolve this, either through direct communication or mediation.
You are not going to get a Guardian Ad Litem on a support appeal in the Virginia Beach Circuit Court. Have you contacted Tidewater Legal Aid to see whether you might qualify for their no-cost legal services for yourself?
Your fiancee cannot adopt your daughter if you are not married to him unless this is a situation (which I feel certain it is not) in which you are giving up your parental rights, and the fiancee would be the sole parent. Courts let single people adopt every day of the week, so that is not the problem. The problem is that two unrelated people-which is what you and your fiance are- cannot be the parties to an adoption.
After a marriage, there is a process for step-parent adoptions set forth in...