It sounds like you are doing great things for your daughter! My family also thought I was insane when I brought up homeschooling, but they’re slowly coming around. Hold on to your own belief that you’re doing the right thing and let them come to grips with it in their own time.
Like Manda said, look up what the actual requirements are. I think NY is one of the stricter states, so you might have some hoops to jump through. (Here in UT, I just have to send a letter to the school saying we’re homeschooling and that’s it; they’re not allowed to ask for any other details. I bet you have to keep a record of subjects and hours studied, though.) However, as far as I’m aware, there is no state that requires schooling before age 6. I could be wrong, but I think you have a couple of years before you have to worry about official paperwork.
So use that time to decide what you want to do! Like Manda said, there are tons of options. One called The Robinson Curriculum got a lot of good responses on BK a while back; search for that thread if you’re interested. It’s nice to have an idea of what resonates with you. I firmly believe that most educational methods will work for someone who likes them enough, so pick what seems best for you, not for anyone else.
While you’re doing your research, your four year old just needs a preschool curriculum. Lucky you, this should be easy. Most preschools teach recognition of letters, numbers, colors, and shapes; fine motor skills like coloring and tracing and maybe writing one’s name, and how to get along with other kids. I’m guessing your daughter knows most of that already. So just keep on with what you’re doing and tell everyone it’s a homeschool preschool. You will probably want to arrange some activities with other kids - playgroups, park days, free get-togethers - so that when other people bring up the whole “social skills” question, you have an easy answer. My daughter actually attends a free neighborhood kindergarten co-op two days a week for two hours a time, for the social exposure. Funny fact, the moms use several curriculum items I used when my daughter was about 18 months to teach the three and four year olds. So she’s not learning anything academic, but she gets to play with her friends for at least an hour of that time and that makes her happy. You don’t need anything that formal, but find some other moms who want to let their kids play together.
Social skills are a whole different post, but here’s a nutshell: people mean two things by “socialization.” One is the basic skills to get along with people: start an innocuous conversation with peers, introduce yourself, do group work with strangers, follow directions from someone in authority, etc. These are definitely teachable at home. You might have to concentrate to make opportunities to practice some of them, but they’re very doable. The other is what Tamsyn (a forum member who was homeschooled and homeschools her kids) calls “school culture.” Going to public school gives people a cultural bond formed around school lunches, gym class, passing time, lockers, etc, that homeschoolers don’t have. Your kids will not suffer for missing out on this! Any more than kids of a mom from, say, India suffer from eating curry instead of peanut butter and jelly sandwiches. It’s just a cultural difference. Lots of people who bring up “socialization” mean the second one, which tends to annoy homeschool parents who don’t think it’s important.
Like Manda says, I’m positive the church will work with you. Talk to your priest and see what needs to be done. She might have to go to special classes through the church for her sacraments, but that shouldn’t be hard to arrange.