I sympathize with your difficulty with multiple cats sharing a household especially if there is a significant difference in ages it is very common to have some cats be more assertive and “bully” others. If they have lived together for a long period of time without incident, it is possible the older cats now have a new smell from underlying illness or weakness that the younger two are reacting to. The older cats may be avoiding the litter box simply due to stress from being bullied, or due to a medical condition such as bladder infection or kidney disease. Even in cases of behavioral litter box avoidance often changes in the house, separate areas for the 2 groups of bonded cats, or in some cases behavioral medications may be used.
The first step I would start with is bringing the older 2 cats in for thorough physical examinations. Additional screening like urinalysis and bloodwork may also be advised to look for underlying medical reasons for avoiding the litter box, vomiting and lethargy. In this age group kidney disease, hyperthyroidism, diabetes, arthritis and inflammatory bowel disease are common chronic conditions, many of which may be able to be managed with medications. In some cases, if there is evidence of a terminal disease or in your discussion with the veterinarian there is determined to be a poor quality of life for her which is unlikely to improve with treatment, euthanasia (letting her go to heaven) may be advised.
We would be happy to schedule an appointment to see your cats at your convenience and decide what the best course of action is for them going forward.