I'm a former staff worship leader from a non-denominational Contemporary Christian Church in Virginia. I've moved across the country and have stepped down from ministry to homeschool my kids. I have been through what you are going through, but I tend to lean on the side of your co-leader and for several reasons. Let me rephrase your questions a little.
Question 1) IS God leading any church to be a particular "style"? Is the singer drawing attention to themself, or is their worship authentic? I think we often get caught up with what is palatable for us and "our" church and sometimes quench the Holy Spirit. You will have to look at the heart. For example, David was a man after God's own heart. He was radical in his worship to the extent that Saul's daughter was infuriated with him and his wife was disgusted. But, David was annointed for this and was filled with the Holy Ghost and ministered to many. The Holy Spirit is what gives us our boldness in Christ. It gives us the boldness and passion to lead others. Many people desire to be in ministry, but they are not annointed for it. Worship is a warrior position. It's powerful! It tears down strongholds and drives out spirits. A timid worship leader/song leader is like a warrior clinging to his sword in fear of the impending battle. I personally feel singer "B" needs the training. The energy on the platform is only reciprocated at 50% by the congregation. The walls of Jericho were not brought down by a handful of musicians.....the whole army was worshipping.
1. What is most important is that you have a true worshipper leading God's people and not a performer. In my experience, personal relationship and knowing someone's heart is no longer a requirement in ministry.
2. What might NOT minister to you, might minister tremendously to another. I strongly feel diversity is lacking in many music ministries and is rapidly segregating churches. Know their heart and why they sing. You may be missing out on a tremendous blessing.
Question 2) Does it create dissension to have a twice-a-monther lead songs that other more committed leaders could handle?
It depends. Is this person asking for special treatment? Are they gigging at bars on their Sundays off or are they ministering somewhere else? Do they get their livelyhood as a musician? Do they have small children and a spouse? All of these things should be weighed. I had a pianist that was a pro-musician and played every weekend. That is how he supported his family. He would love to be on staff at the church, but we couldn't afford him. I accommodated his schedule because I knew his heart, he just had to make a living too. It really boils down to their heart. If they are a true worshipper, Christ-centered, grounded in the word, a true spiritual leader, and exemplary in their walk; then make room for their gifting.
May God bathe you in wisdom and annoint you with discernment in your decisions.