Brains are irritating things!
I have generalised anxiety disorder and so understand your concern, Brivaracetam definitely hasn't made this worse for me and I didn't notice any particular worsening of my MH either. I'm so sorry about your dad, my mum died about a year before I started taking Brivaracetam and the thought of adding something that could potentially destabilise your mood further is a legitimate worry.
My side effects experience was complicated as I was reducing antidepressants at the same time as starting Brivaracetam - I cannot recommend this! So, it's difficult to know which side effects were solely the AED. The whole side effects period lasted no more than 4 months (I think it was less than this but I can't quite remember). I mostly recall being very sensitive to noise, feeling like I was going to fall over, lots of dizziness, just generally spaced out and I had to nap quite a bit during the day. My DH did lots of the school runs and if I had to I'd get a school runner friend to walk with me, just in case. As I said, though, do remember that my experience included antidepressant withdrawal and it might not be so intense for you. Once I was on the final dose, the side effects dissipated quite quickly, I think.
I'm a plan for the worst type of person, are you able to put loose plans in place to help you to cope if necessary?
Please don't be terrified, think of the end game, it was so worth it for me. Have you ever been on Keppra? This was the worst for me and I had to abandon it after 2 months because the side effects were too severe, Brivaracetam was not nearly as horrendous as Keppra!
Can I ask why they've taking you off lamotrigine? I'm still taking lamotrigine as well, 100mg. Various clinicians always mention that it's mood stabilising, I've never noticed it, even when I've been on a higher dose!
I hope what I've written doesn't put you off, once you can get through the initial period of crappiness, it's so worth it.