Only God knows whether or not your uncle truly believes in Jesus -- but one thing is clear: His inconsistent life not only displeases you, but it displeases God.
In fact (as I've often pointed out when people accuse Christians of being hypocrites), some of Jesus' strongest words were directed at hypocrites -- at those who claimed to believe in God and follow Him but didn't show it in their lives. He said of them, "These people honor me with their lips, but their hearts are far from me" (Matthew 15:8).
When we try to dominate those around us and deal with them harshly, we fail to keep Jesus' command to treat others the same way we'd want them to treat us (see Matthew 7:12). We also are failing to demonstrate God's love for them, as Christ has commanded us to do. The Bible says, "Love is patient, love is kind.... It is not rude, it is not self-seeking" (1 Corinthians 13:4-5).
At the same time, remember that Christians aren't perfect -- nor will we ever be until we enter heaven. But God still loves us (just as He does you), and He accepts us just as we are when we come to Christ by faith. Don't let the failures of a few keep you from Christ, or use your uncle's inconsistency as an excuse to reject Him. Instead, face your need for His forgiveness and commit your life to Him today.