Hi, I'm Dr. Bonk. I'm sorry to hear about your kids' issues. There are several processes that can lead to the symptoms you are describing.
One would be a selenium deficiency. Selenium and vitamin E are needed for proper muscle function. A deficiency can cause symmetrical muscle damage in the girdle and limb muscles leading to an inability to stand. Most soils in the US are deficient in selenium leading to plants that are deficient. Therefore, the only way animals acquire selenium is through supplementation in mineral blocks or by injection. Bo-Se is a selenium and vitamin E injection found at most veterinary clinics and possibly feed stores.
Secondly would be a thiamine deficiency. However, this one usually causes changes in mentation and appetite as well as ataxia and partial paralysis.
Finally, another cause would be Caprine Arthritis and Encephalitis (CAE). This typically causes arthritis in adult goats, but encephalitis in nursing kids 2-4 months of age. It typically starts as lameness and ataxia that progresses to para and tetraparesis and paralysis. They can also develop pneumonia associated with the virus. There is no real treatment besides support care and antibiotics to help prevent the pneumonia part. The doe may show signs of mastitis with this as well.
You can start by giving supplemental injections of both Bo-Se and either a thiamine or vitamin B complex. There are serology tests available for CAE to that are somewhat diagnostic if the supplements don't work.
I hope this helps. Please contact me with any further questions you may have. Thank you and good luck!