To be honest with you, up to about 5th or 6th grade you do not really need a formal curriculum. And certainly not for 2nd grade. What you do need is some sort of structure so they get used to routine. But for the younger folks you can turn almost anything into homeschooling. A walk around the neighborhood can become a math lesson as they count or categorize cars in driveways, or the average number of cracks in the sidewalk.
One thing that is important, though, is a structure that makes sure you are covering the important things. We found the book series “What your xxx grader needs to know.” It presents an outline of topics in a logical way to build up a well rounded education. They went up to sixth grade when we were at that age. But anything like this would give you the confidence that you are not missing the critical stuff.
The other thing I would suggest is to focus on the basics - reading, writing, ciphering. Ok, second grade not so much ciphering, but they should be on their way to learning the times tables (or the concept behind them). But if they learn reading above their grade level, and start writing, that will give them the tools to move along later.
Find books just above their age and read them together out loud. Fun books, because reading should be fun, not a chore.
Meanwhile, dive in, remember that well over 50% of the public school day is administrative and not education, and have fun covering in 2 hours what they used to cover in 6.
Let me just say that ‘structure’ has to be taught. Some children have no structure at home. I had a mom who worked to feed four kids after my father died from war wounds. When teachers handed out homework to do I had no help at home nor understanding of what structure was other than mealtime and bedtime.
An Aunt died and left her desk to my mother.....as a kid of 7 yrs old I thought if I sat at that desk, in that bitter cold corner of the room, it would make me smart as she was a teacher I had never met.. ......I write this because the longing of a childs mind and heart to learn, to know how to learn, is not always recognized.
Grades throughout school years were barely passing and I stuggled, embarrassed that I couldn’t grasp “learning” as other kids did. It was not until I was married at a young age (18) with two children I decided to go to a business school that I aced pretty much everything.....my environment was mine to control then.
I write this because there are children who are much smarter than they realized, and are indeed ‘left behind’ when basically on their own on the homefront at the tender years of growing up.
I learned....but it was later years and still am learning.