Like you, I have found brushing my cats teeth with a paste and a toothbrush too stressful for them and gave up with it.
Once a cat is at the point of having tartar on the teeth which then goes onto cause inflamation of the gums (gingivitus) I would say you are going to have to take the advice of the vet and let her teeth be cleaned.
Be prepared that they may take out some teeth - but a vet would only do this if essential.
Well you need a vet you trust and can talk to.
Personally I think it is best to let the vet clean her teeth as untreated gingivitus can lead to more health problems.

You are not going to do much good cleaning her teeth at this point in time - it won't get rid of the tartar or the gum inflamation.
Once the teeth are cleaned you could have another go at teeth cleaning to maintain what the vet has done.
Or try a dental food like has been suggested.

I'm afraid I've found it difficult, I never managed to clean my cats teeth, and I relied on my vet to clean them - in their lifetimes (to 18) each cat went under anesthetic twice for cleaning - but if they ever have to go under for another reason - you can always ask the vet to clean the teeth at the same time.

If your cats are young and would take to a raw diet that included bones their teeth may stay cleaner for longer - I'd be interested if any owners feeding raw diets could say if a raw diet helped to keep teeth in better condition.