First off, I'm a complete novice at modding and using the CK.

I've changed Brelynas class, spell list and perks, but she won't cast anything during combat. Completely unsure as to why, exact changes are as follows

Removed all her vanilla spells and perks, added a custom class, removed her outfit.

Spell List:
Summon Frost Atronach
Summon Flame Atronach
Summon Storm Atronach
Dread Zombie

Perk List:
Conjuration Novice
Conjuration Apprentice
Conjuration Adept
Conjuration Expert
Conjuration Dual Casting
Atromancy
Necromancy
Summoner70
Twin Souls
Dark Souls
Elemental Potency

Things I've tried are using left and right hand specific versions of the spells and changing her class back to default, neither of those have helped and I'm at a bit of a loss as to what else I can do to troubleshoot the issue.

Starting a brand new character also did not resolve the issue.

Changing her aggression levels and confidence also didn't fix it.

Ummm you went to an awful lot of trouble to put her down the Conjuration path, (which she is already on) you've listed one extra spell she doesn't have normally, Dread Zombie, though I have no idea what her vanilla perc picks are.

I'm going to expand her further down destruction and restoration, but I wanted to test if she would at least use what I gave her so far and it turns out that she doesn't and I have no idea why.

Okay, so I also decided to give her Conjure Familiar, which she casts without problems. She just won't summon any of the Atronachs.

That's odd because she summons Frost Atronachs all the time for me, good wifey

Yeah, it's highly frustrating. Her conjuration skill is at 100 so it's definately high enough to cast at least Flame Atronach, and I gave her 5000 magicka for testing purposes. Wonder why she won't cast it.

You've changed too many things at once to be able to problem solve what's going on cleanly. I suggest you go back to her vanilla starting point (new esp) and change one thing at a time. Also, I wouldn't add more than one atronach per level. I think that might be "confusing" her, or at least don't try it until you have, say, the flame atronach working when her skills are in the right window so that you can see that you've got something working. However, if you have her conjuration skills set at 100 you should see her only casting the highest level atronach. She will no longer cast the lower level spells once her skills are high enough to use a higher level skill. This will be true of any skill and spells she has in her lists. At least this is what I've seen in my testing/experimentation with Marcurio. Also, perks don't necessarily work with NPCs so you might experiment with one that is obviously going to show whether it works or not and do some testing with that one only. Also, be sure to keep her using a magic using class.

Unfortunately, changing her back to her vanilla setting was something I tried and she still wouldn't cast any of her atronachs.

I have however added different spells, she's perfectly happy to conjure a familiar and use firebolt, flames, healing spells and wards, the only thing she absolutely will not cast is the atronachs which is peculiar. I also took a gander at the (recently discovered) discussion tab on her UESP page and some people have reported that she won't cast atronachs for them, either, yet for others she does. It's very unusual.