"Take heed to yourselves. If your brother sins against you, rebuke him; and if he repents, forgive him. And if he sins against you seven times in a day, and seven times in a day returns to you, saying, ‘I repent,’ you shall forgive him" (Luke 17:3-4).
After reading this passage, it causes me to believe that one does not forgive a brother if he sins against you until that brother repents and asks for forgiveness. Which to me is entirely logical since God does not forgive us until we have repented and asked for His forgiveness. Am I wrong in understanding the passage like this?
My wife and I did not agree with clapping by the song leader in our congregation when he led songs and encourage others to clap. We met with two of the elders and expressed our view. We were told to "go on down the road" if we were unhappy. Since our children and grandchildren attend this congregation too we feel compelled to worship there to support them. Neither of the elders has ever asked for forgiveness. But maybe we were wrong in being offended by the clapping.
In answer to the question about whether repentance is required for forgiveness, see Does a person have to repent before you can forgive him?
In regards to clapping in worship services, see Should my objection to clapping during singing be respected as a weaker brother?
The men you talked to are not convinced that clapping in worship is wrong; thus, they don't believe they have anything to repent about. They made it clear that they aren't concerned about your views and they are not willing to seek a way for all to worship together.
If you are convinced that clapping is not authorized by God, why are you considering supporting family members in doing something that you consider to be wrong? God has to come before family. "He who loves father or mother more than Me is not worthy of Me; and he who loves son or daughter more than Me is not worthy of Me. And he who does not take his cross and follow after Me is not worthy of Me" (Matthew 10:37-38).