As mood stabilizers go, Tegretol is one of the older ones, but there are newer and (IMO) better ones available. But your doctor knows your full history and there may be reasons for not putting you on a different one. My daughter was on Trileptal for a while (second generation Tegretol) and it didn't really do much for her. I have had good results with Lamictal (same class of drug as Tegretol) and it has been shown to really help with bipolar depression, so maybe that's an option? The Tegretol may not be enough to oppose an antidepressant and you may need something stronger like Depakote (valproic acid) or an antipsychotic.
As for IOP, I have had good luck with them. They are called "partial hospitalizations" here where I am. I have actually found some of them more helpful than inpatient, when I've been safe enough to be outpatient. You typically get more groups per day than inpatient, and they are generally more involved than the inpatient groups I have had. And the nice thing is that you get to go home afterwards and practice what you have learned in the context of your normal stressors rather than the protected environment of the hospital.
As for your mother, she may not be a good support for you now. Now might not be the time to try to educate her, at least not until you're feeling better. Lean on the supports you know have been beneficial, and definitely come here!

We may not be right there with you, but it's a good place to find people who understand, especially at 10:00 at night when your other supports might be unavailable.
Hang in there - you'll get through this.