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I hear you loud and clear. Often times when a person suffers from a thought disorder and/or a substance abuse problem (which your sister seems to possibly have both, given your description), they are too paranoid/suspicious to trust ANY intervention, let alone one which seems to be pushing them into a direction they do not want to follow (i.e., hospitalization or medication). Too, the alcoholism alone will be staunchly defended by the substance abuser - they dare not think of living without the alcohol!
But your question is also well founded. Here are my suggestions:
(1) Wait for a physical ailment to crop up - or perhaps wait until she is in need of a yearly OB/Gyn visit. Accompany her to the doctor and be certain to mention the other issues relevant in her life. As odd as it may seem, even paranoid folks will acquiesce to going to the physician if there is a physical malady (broken bone, flu, etc.). Despite their paranoia, the more primitive survival instinct may over-ride the suspiciousness.
(2) This seems a bit more under-handed, but if the animals are indeed in jeopardy, then getting the police involved may be enough leverage for her to take a look at her situation and agree to getting help. Animal control here in the States usually tries to work with owners to help them access the services they need. And if there are potential charges or court action pending, then she again may muster the drive to seek help.
(3) If she is getting money of financial help from any of the family or friends, make the continued support contingent upon seeing a doctor. She will hate this route, but again, survival is a powerful drive.
(4) and finally, because we cannot technically "force" an adult into treatment, we can use whatever leverage is available. One model is to attempt an intervention, whereby the important people in her life gather and list the reasons they feel she needs help, and then list the consequences they will adhere if she does not comply. I listed this one last because it is less likely to work with a person who really does NOT care about relationships. Still, her animals (see #2 above) or money (see #3 above) can be lumped together alongside other pressure points to urge her into treatment.
I know there are not good answers, but I hope these provided at least one idea you have not thought about. If you are satisfied with the response, please hit "Accept. That is the only way i receive credit for my answer. Thanks-