My husband does not like the idea of hiring a yaya who has a strong Visayan accent. How can I convince him otherwise?

Children who are just beginning to learn how to speak do acquire the accent of whoever speaks with them most of the time. There is a possibility that kids may copy that accent of their yaya, but this will not be permanent.
If you are there to correct your tot’s pronunciation and accent, even grammar, and she is able to interact and communicate with different people other than the yaya, then you should not be worried at all. What is most important is the yaya’s dedication to her work and her love for her alaga.
Rather than fretting over her accent, it’s her manner of speaking and the words she uses with your child that should be given focus.