OMG, they are too cute!!
I used to volunteer at a NYC animal shelter (it was a kill shelter) in the Cat & Kitten Rooms, and kittens never got put to sleep as they were ALWAYS the first to get adopted. (the only times they were euthanized is when they were too sick to be adopted or were dying) The younger they are, the higher the chances of them getting adopted, so I wouldn't be discouraged from bringing them to a public shelter, even if they euthanize their animals. Their chances of getting adopted into a loving home are extremely high.
Looking at their fur, they also "look" very desirable as well. At the shelter I volunteered at, a disproportionate number of adult black cats were euthanized as no one adopted them due to ignorance and just dumb superstition - i.e. black cats are bad luck nonsense. Adult cats with less common fur colors (calicos, orange, fluffy fur, interesting fur patterns) were usually the first to get adopted. (The animal's personality was second for most ppl)
Also, at least in NYC, all the local no-kill rescue groups get a lot of their animals from city-run shelters, like the one I volunteered at. Obviously, they'd only take the most desirable cats and dogs (pure-breds, puppies, kittens), so these little guys may get taken in by a no-kill rescue group that way too, if LA shelters have the same kind of system.
Even if it means separating mommy cat and her kittens, I definitely would not bring Mommy Cat in because they will most certainly get separated at the shelter, and the chances of her getting euthanized is sadly high, since she is an adult cat.
With kittens, a few weeks can make a big difference (the smaller they are, the better the chances of them getting adopted - at nyc shelters, kittens are put on adoption display at 6wks old) Also, if they have some kind of illness that will delay their adoption display, that will decrease their adoption chances as well, so I'd bring them to a shelter that will take them as soon as possible. Not sure if any of this is new knowledge, but hope it helps and a huge thumbs up to you for taking them under your wing.
