At this time, there are three possible approaches to your issue of resolving the closeness of your relationship to your (presumed) cousin.
- Good old-fashioned detailed analysis and interpretation of the documentary records backwards through as many generations as is necessary for your particular circumstances. The grave disadvantage is that by the time you answer the question, you and your potential partner may be too old to care.
- Comparison of genetic material (both chromosomal and mitochondrial). This will give you a rapid answer. Unfortunately, this answer will be definitive only if it is the one that you do not want. DNA will tell you with some certainty that you do share a common ancestor at generation X, but any statement that you are not related must be hedged with uncertainty (if the vendors are scientifically honest).
- Consult with the culturally-endorsed keepers of the old lore. This also allows for the fact that our common (western) assertion that kinship equals consanguinity is not universal. Other ethnic and cultural traditions choose to prohibit associations between individuals who europeans would regard as unrelated.
Before you send off your cheek swabs for analysis, you need to determine whether (future) father-in-law will regard the results as acceptable "evidence" in this context. If he does not, then you will have purchased some interesting information that does not actually advance your position.