We have done both and right now both my boys are in school (K and 2nd). My first homeschooled for K and my second is in full-day K. He loves it. I don't think your child will be labeled a problem child just for having a bad day. Both of my kids can be difficult IMO but their teachers say they are always kind, polite, hard-working, helpful, etc. My kindergartner's teacher told me he is "always on the side of good" and he is my most difficult child (we butt heads).
My kindergartner has "stations" in his class which include a nature table, painting, draw/write, computers, home (play kitchen/dressup), water, Legos, etc. The teacher works with small groups on their "lesson" while the other kids play. This makes up the majority of their homeroom time. They also have science, PE, spanish, art, music, library and computer lab (all multiple times a week) along with lunch and recess.
My 2nd grader always resisted learning at home. He doesn't listen to me the way he does at school. He started public K behind in reading/writing and ahead in math but quickly evened out in both. He is very social and fits in wherever he goes; a good school environment works for him. My little guy is a self-led learner who would do great at home but he does not EVER want to homeschool. He loves school despite it not meeting all of his academic needs.
On the values thing, I guess I'm just pretty confident that we are right and they'll see that. We aren't non-vaxers but as far as the way we eat, etc. it hasn't been an issue.
You can know as much or as little as you want to about the curriculum and what goes on there. The teacher will give you his/her email and probably phone number. They send home newsletters or have a website or both. They'll tell you what curricula they are using and the school district should have info on grade standards online. You can volunteer in the classroom. You can be a room parent. You can stop by to observe. I had a regular day that I volunteered in my oldest son's 1st grade classroom (Mondays from 9:30-11) and am starting in my K's classroom next week (Wednesdays from 8:50-11:20). Schools welcome parent involvement.