First of all, this does not qualify as abuse. Not teaching your children (or teaching your children, for that matter) is no where close to abuse. If the child were being beaten, that would be a completely different situation. Honestly. Throughout the world, millions of children grow up without adequate education, and no one claiming they are being 'abused.' While it may not seem very nice to you, it fails to meet the basic qualifications of abuse.
Neglect, you might have a small bit of leeway there to say it is neglect.
However, that is only possible with the oldest 2 students, even if you tried. The other 2 are not legally required by law to go to school, and therefore are exempt.
Your state laws say "A school that is nonpublic, non-accredited, and not otherwise approved by the Indiana State Board of Education is not bound by any requirements set forth in IC 20 or IC 21 with regard to curriculum or the content of educational programs offered by the school."
Basically, what that is saying is that they have to comply with very few laws, since they are not public or accredited, nor are the approved by the board of education. They have to meet with a minimum days of instruction, but they have no required subjects to teach (not even reading is required).
So, no classes are required by your state, nor is any testing required by your state. The only thing required is that they report and that they keep track of attendance.
I know to a person who places a high value on education, this seems just beyond bizarre.
But, the truth of the matter is, if they are reporting and keeping track of attendance, they don't, by law, have to do anything else.
Education is not a "basic need." Basic needs are food, oxygen, water, sleep, hygiene, basic safety.
If the parents are providing these things, building a case for neglect is going to be very, very difficult indeed.
Also, I wouldn't be so quick to ensure that public schools in your state all do that great of a job either. Some schools, yes. But, in all states, there are school who simply learn to work around the rules. A parent can refuse standardized testing, and they can refuse special education, and they can refuse IEPs. Children are not required by law to take standardized tests.
Also, many schools recognize that some students are simply not capable/willing to pass. So, they learn to work around the rules, creating IEPs and specialized plans for those who are not going to pass, so they can increase their pass rates, especially since they will get extra funding for these students, and look better in the process. Which is even more important with more "No Child Left Behind" laws that are coming into effect each year.
My own brother lives in a state with a reputation for one of the best educations in the country (at the time of his graduation), and he was allowed to pass and graduate from high school, reading at barely a third grade level, because he qualified every year for IEPs and special education, and he didn't have to take the tests, because they knew he would fail, and they wrote the into his learning plan. The only learning disability he had was dyslexia.
But, that is a different topic.
What can you, as an aunt, do about this?
Honestly, not much. You can offer your services in teaching some subjects, you can offer to purchase curriculum for them, you can offer to help in any way you can. Maybe ask to move in with them and take over the teaching under their supervision. Ask for your niece once a week to teach reading. Pay for a special tutor or for testing for visual processing disorders.
But, you can't force people to comply with your values.
We all wish we could. We all wish people would just quit doing things that we don't approve of. But life doesn't work that way.
I wish people around me would quit swearing, especially parents with small children. But, I can't do a whole lot about it, except ask them not to swear.
Same with education. If they don't want their children to be taught, there isn't a whole lot you can do about it. Despite the fact that you feel you have a moral, ethical obligation, the state is saying that really, you don't. The state doesn't even reserve that right for itself. It clearly states that they are backing down on that.
So, I hate to be the bearer of bad news, but your hands are pretty much tied. Unless you can convince them to move to a state with more strict homeschooling laws.
Your state does not consider reading a requirement. Or math, or science. So, your values and mine don't play into effect here much. Your nieces and nephews are allowed to grow up as ignorant as their parents want them to be.
Now, if you see other signs of abuse or neglect, you may have more of a case, in conjunction with the lack of homeschooling.