My Neurologist told me that Lamotrigine has less serious side effects than most other AEDs. I haven't had any issues with any of the things you mentioned, like weight gain, or blood tests in the abnormal range. I have labs done a few times each year, and everything is always normal.

My rashes have been varied with the most memorable being dark red patches on the back of my knees, small itchy red bumps on my thighs, and barely visible slightly burning blisters on my face. The worst thing about them is that they last a long time, but that's just how my body reacts to Lamotrigine. Take into consideration that I take the lowest effective dose -- 100mg, 2 x day, so I have no idea how my body would react to a higher dose.

The Mayo Clinic has an online page with the side effects listed as most common, less common, and rare. It's the most comprehensive list that I've seen. Here's the link:
https://www.mayoclinic.org/drugs-supplements/lamotrigine-oral-route/side-effects/DRG-20067449?p=1
You'll have to scroll down quite a way to find the lists.

I truly hope that you find the best treatment for your daughter. I can't imagine how challenging it is to have to make this sort of decision for her, especially since she's nonverbal. It sounds like you're asking the right questions, and taking every precaution. She's fortunate to have you looking out for her.