Ok, I am reacting here a bit because I am going through a similar rough time with my inlaws. I am not in the least angry with you or anything, but right now, this is destroying our relationship with them. If I can stop this happening to another family, I want to do that, even if it means me saying things that don't sound nice. I figure you can always ignore me, but perhaps it there will be stuff in here that is helpful.
Here is the thing. It is so utterly HORRIBLE having someone constantly questioning what you are doing, suggesting that you are sending your child on "a path to the dole because she has no education", buying books, etc. The equivalent would be if your MIL was attacking you because you had sent your kids to school, turning up with workbooks, questioning whether you were committed or capable enough to make sure that your kids didn't chuck their lives away.
Here is what you could do if you are concerned and want to know how much your SIL actually knows. Start (or continue) to take an interest in her. You think she should go for walks-take her for walks! Find out what common interests you have, or what you do already that she might want to do, and try to develop a mentor-type relationship.
In my family, ds, who is 4, has two big interests atm-electronics and tudor britain (especially the great fire of london, for some reason!). (I mean he is interested in all the usual stuff, but those are the books he takes to bed with him).
FIL is a physics teacher and MIL is a history teacher. Our specialisms are biochemistry and mathematics, (and even more uselessly, we both had/have legal careers too) so these are known weak points for us. We can keep up with a 4 yo, but are probably going to need to find a mentor for him if these interests continue.
Now if PIL were to spend the time they spend going on and on about ds's lack education on reading books with him, building circuits, etc etc-THAT would be so wonderful! He would love it, I think they would love it, and as real enthusiasts, who do this kind of stuff outside work just because they love it, they would just have so much potential to advance his interest and knowlege. As a bonus aside they would see how he learns stuff-he's teaching himself to read from circuit diagrams, for example, and has gotten interested enough that he's asked us to teach him "properly" (I think he means "more quickly". Of course we will, and are just looking into which method/workbooks are likely to suit him best atm).
BUT they don't help, I think because they are not trained to teach primary (they think that there is a "correct" way to teach anything). But also because they disaprove and would see helping ds with his interests as colluding in our mad scheme.
At the same time, my family, all of whom are teachers also, have been incredibly supportive and I have seen the benefits to both them and ds in them sharing their interests with him. My brother is an electronics whizz and loves to share this with ds, and this has been incredibly beneficial, not just in terms of their relationship but also because ds has learnt so much-he has had 1-1 attention from someone who loves electronics.
I am serious, this is ruining our relationship with my kids' grandparents. I feel right now that my choice is between constant, really nasty, family rows, and sending my kids to school. We are seriously considering massively reducing contact, which would be an incredible shame.
Please don't let that happen to your family. Please take a really hard look at how you might be coming across to your MIL and, even if it means standing down on your principles, think about whether you can approach it differently.
I do hope this helps.