Yeah I think this is a good idea at this point. You need to be able to get your point across and feel listened to and it sounds like you're going to need someone to help you with that.
Drugs are not always the best way to manage depression and she really seems to need more help than what she is getting from her psychiatrist right now.
The problem with counseling is that the person has to want the help. It will fail 100% if Chaos goes willingly but his wife could give two shits because of whatever emotional or psychiatric reason.
Chaos, at some point you will have to be blunt. She has led you on for two years. My Dad's side of the family all suffer(ed) from terrible anxiety. I went through the same bullshit therapists and drug regimen as a young kid because it was just 'part of dealing with the problem' before anyone knew I had a problem. When I was a young teenager, during one of my 'fuck the world' type of moods I decided that it was not the path I wanted to take and ditched it. Wrong reasons, lots of fights with my parents about not seeing the therapist anymore, but good results. I pushed myself to do new things, face my fears. I still have the same feelings, but I've learned how to manage them like a normal person. It took many years, but I attribute some of that to the fact that I was growing as any person does in those years. Today, I feed off stress and adrenaline as indicators to focus and rely on confidence in my abilities instead of just letting it stop me through crippling inaction - which is exactly what they are. Markers to tell you to get your shit together because you aren't doing something easy.
There are people who truly do have legitimately severe chemical imbalance that need drugs to cope with depression or anxiety. In my experience, anecdotal though it is, the VAST majority of them are not those people. Instead, they enjoy the excuse it gives to continue acting inappropriately. Even with the drugs they practice self-defeating ways of life. They look at a long project and start crying and claiming they are too anxious instead of tearing it down to base components and getting their ass moving, one step at a time. They want help for everything. When you manage their task, they are clearly able to do the individual parts, but they will get emotional and violently angry if you share your observations that they can accomplish exactly what they said they could not. They claim to be overwhelmed by stimuli instead of simply first managing the ones they can and tuning out the ones they can't in order to focus on a task. They need to, quite simply, unfuck themselves. No amount of drugs is ever going to teach people how to actually manage the root causes that lead to anxiety or depression. They just treat the symptoms.
If you want to keep applying burn cream, keep on with drugs and therapy that she clearly isn't invested in. If you want to actually force her to learn how to handle fire, set some rules and give some ultimatums. You will have to be prepared for some serious things to happen, like the eventuality that you could divorce. Your wife very well may rely on the safety of her position to defend to herself why she doesn't need to actually work through her problems. You may have to start following through with your ultimatums to show her how serious you are and that it isn't acceptable to just give up and take drugs while lounging around lamenting about your current situation. But what you're doing right now is preemptively plugging your still living relationship into life support instead of figuring out how to treat it. I wish I could convince my father to stop coddling my brother EXACTLY like you are coddling your wife (with the exact same diagnosis). He means well, but at some point you have to pull the umbilical and help them work it out instead of just manage the net effects of their shitty life choices.
I will tell you one very real threat to your children that I saw first hand: If you do not help your wife change or remove them from her influence, they will be turned down the same road. Again, nothing to do with chemicals in the brain at all, but rather with very learned traits and reactions. They will learn to cope with stress by being angry and withdrawing, or learn to handle all problems by turning to others before even attempting to solve them themselves. They may not be able to logically connect it all, but children are not stupid. They will start to put two and two together and eventually realize that they will simply be rescued every time a challenge comes their way (like Mommy) and they will act accordingly.