If I was arrested for stealing my mother’s gun while living at her residence and now I’m charged with felony theft, what are my options?

You have several options depending on how your mom feels about the situation, the extent if any of your criminal history, and the attitude of the local prosecutor.
If your mom understands that you took it and that you are willing to help her get it back, then your mom may agree to drop the charges all together.  She would need to sign an affidavit of non-prosecution.  The prosecutor may also need to visit with her to confirm that this is not an ongoing issue, but rather an isolated incident.
If your mom won't drop the charges, then much of what will happen depends on your criminal history.  If you don't have an extensive history, then you would be a good candidate for probation or a reduced sentence.  For example, you can try to plea bargain so that you enter a plea for a misdemeanor theft, rather than a felony theft.  If you receive a probated sentence, then you will not be required to spend time in jail unless you do something to violate your conditions of probation.
If you have an extensive history that includes a prior felony, you may need to work hard to obtain a felony probation.  With a prior, you would be considered a prohibited person in possession of a firearm... which is a felony under federal laws.  Prosecutors tend to be less lenient on defendants with extensive criminal histories.
You note that you have tried cooperating with the police.  Sometimes cooperation can help work things out, but frequently, when people cooperate they simply end up making the police's job easier with statements or confessions.  You may want to continue the cooperation, however, I strongly recommend that you hire an attorney to assist you with the process.  They can make sure that you don't waive any valuable rights.  If a "deal" is offered, they can make sure that it is properly recorded so that you will have a way to enforce it later.  Just because an officer promises to "help you out", doesn't mean the prosecutor will honor the agreement.  Without the proper documents, the prosecutor won't even be required to honor the agreement.