The big problem with doubters is that they can shake your confidence. Make an effort to meet as many other homeschool families as possible. Spending time around other homeschoolers will help you feel confident about the choice you're making and allow you to see how people with vastly different lifestyles and methods of education have great outcomes. Getting a boost of courage from experienced families in the beginning will help get you started, and after you've been homeschooling for a few months, you'll be able to build on that boost with your own experience.
If you feel you need to appeal to family and friends, one good approach is to ask them to help. If your sister is a nurse, you can say "Hey, when we get to anatomy, your expertise is going to be essential." Even if you never do get around to picking her brain, getting people on board gives them a stake in your education plan and brings them around to your side. Almost everyone is an expert at something and chances are, they want to talk about it.