Ds1 has only just found the speech sound "L" - you could have been talking about him aged 3. He is nearly 5 now, and although his speech is still indistinct sometimes (He will say "You do i' like 'at!" instead of "You do it like that!") he is, in the main, keeping up with his peers.
It did distress him sometimes when his peers couldn't understand him, but the best thing I found to do was relax, do Jolly Phonics (these really really helped his speech sounds, funnily) and just wait.
At 3, she may not be old enough to understand some of the tricks the speech therapists use to help the sounds come. To help ds1 find L, the SALT got him to 'break' words - so "LLLLL - ight, llllll - orry, llllll - lick" etc.This relies on the child (a) having the concentration to listen to, understand and follow the instructions, and (b) enough understanding of word structure to know that words are made up of different parts.
The babble will clear up, if she is anything like ds1 (and she does sound a lot like him).
I found it difficult to stress to the playschool staff that if ds1 had pushed someone because they were being mean, it's not as simple as"Tell a teacher" when the teachers don't understand him. Make the staff aware that she is feeling frustrated socially and may need some support until she is struggling less (which I hope will be very soon)
And finally - I remember this feeling. It is nothing you have done wrong. Please don't wind yourself u to the point where you are dreaming about poking coins unto your child's mouth to make it 'work', as I was last year!
I know it's heartbreaking, but next year it will all be so different - the babble is a good thing in a way - it shows she has the urge to communicate and at least some vocabulary. The clarity will come.