Desensitizing an adult dog can be a challenge, and may have limited results. Hopefully, you got there on your own already, or saw a trained dog professional for help.
Also, is 3yo otherwise noise sensitive, or just to a particular type of report, say 12 ga vs 28 ga or .22 vs 9mm? What breed? Amleor female?
Do what we do with puppies first, and see how it goes. It should improve her response.
Short term, you can place earplugs or cotton balls in 3yo years (yes, you can, it is done, especially with retrievers hunting from your side). Their eardrums are much farther in the canal than humans.
What we do is have the report be a positive stimulus (Pavlovian-like behavior modification). As dog is first fed, make noises by dropping heavy books, pans, etc in other room or at a distance. This assumes dog is fed on a schedule. It will not work if they free-feed. You may need to withhold food, and then feed once a day - twice a day once things get going.
Once this is tolerated, in far room/distance, fire off toy cap gun - the kind with paper roll or tiny cups. Over time, try to get in same room. They should not care, and focus on food bowl and eat. If they show concern, you have moved steps too quickly. Go back to previous step.
We eventually fire a primer pistol, pointed away from them, right next to them while being fed. Using .209 shotgun primers in a modified revolver. They could care less.
Then, we start the same feed/shoot process outside, with the 209 revolver at a distance, then close as before. Follow it with a 20 ga at a distance, then up to 10 yards close - always pointed no closer than 45 degree angle away from them. Follow it with a 12 ga, same method.
I had a dog that LOVED to hunt. Would rather hunt than eat - would spit out treats if on a hunt. BUT, bring out a 870 and rack it, she would head back for the crate. She got over that by putting her bowl down then racking the slide ONCE. Within a short time, she got over it, as we increase the number of times to rack the slide.
Slow and sure wins the race. Some dogs never fully enjoy it, but if their focus is on something they REALLY enjoy, and the stimulus (gun report) becomes a sign for what they enjoy, your problem should be close to solved.
If you try things on your own, no no avail, then you may need the hands-on expertise of someone to analyze the situation, and make a recommendation. Some calming Bach Rescue Remedy added into the process for 3yo may help things along.
But it sounds like 3yo is no super freaked, but just does not understand fully what the sound is and from where is it coming.
HTH
