Question: "Is it wrong to have a relationship with a close relative?"
Answer: The relationships that God forbade in the Old Testament Law are listed in Leviticus chapter 18, verses 6-18. In that passage, we are commanded not to marry a parent, a step-parent, a grandchild (and, understood, a grandparent), a sibling, a brother or sister of a parent (i.e., an aunt or uncle), or a half-sibling. Marriage between cousins is nowhere forbidden in the Bible.
In the very early days of humanity, there were a limited number of human beings. As a result, marriage between close relatives was often necessary. It was not until humanity increased greatly on the earth that people no longer needed to intermarry among relatives. In the early days of humanity, the human genetic code was not corrupted to the extent that it is today. Therefore, it was safe for close relatives to marry and have children. There was little risk of genetic abnormalities in their children. Once the human race expanded and, due to sin, the human genetic code became corrupted too much, God commanded against the marriage of close relatives.
So there is nothing essentially evil about marrying a close relative. The reason we should not do it is that it is unsafe genetically. Further, most nations today have strict laws against marriage between close relatives. The Bible commands us to obey the laws of the nation we live in (Romans 13:1-6). Most laws recognize second cousins as sufficiently separate to allow marriage. Any couple that is related and considering marriage should pray wholeheartedly for God to give them wisdom and discretion as to whether it is His will (James 1:5). A couple should most definitely consult their families about the matter as well.