Two things that helped someone I know of in a similar circumstance, FWIW:
1. He had an undergrad degree from OM and had taken a class from a law prof in the Croft.
2. His family had owned land in MS since 1803.
At the very least, you should make an appointment to visit the law school and speak with the admissions department. I think OM has a question on its application regarding relatives that have attended OM.
I went through this process as well, when it is all said and done it the LSAT, GPA, and quality of undergrad school/program dictate admissions. Better the LSAT, better chance of getting in.