We have inherited a big berberis under a huge ornamental flowering cherry in our front garden.It has flowers & I constantly trim it as its a danger to passing children to & from school etc So far this year trimmed 3 times & its in its normal shape but most of the old leaves have been eaten by tiny yellow striped snails. In 22 yrs never seen anything like it !! Caught red handed!!
You're going to have to lay waste to those suckers. I'd find a systemic insecticide with imidacloprid as the main ingredient. You mix it with water and sprinkle around the shrub. If the plant currently has flowers, you'd best wait until it was done flowering as this chemical is toxic to pollinators. It should be out of the soil by the time the plant flowers again.
We have a dog, nbrs cats & there are a lot of birds in front & back. I have some chemicals in a secret place. The dog can not reach them.