I feel I can relate somewhat to what you're going through, tasryn. I, too, have an overly "helpful" in-law in my BIL (my sister's husband).
On the one hand, you know how they are. They want to be part of your life. They want to help. They can also be a little bit overbearing. They can be bossy. They have all the answers. Except, their advice is usually the wrong advice - because they only half-listen to the problem and jump to conclusions. (At least in my BIL's case). You don't want to alienate them. You don't want them to feel unwelcome...and you don't want them to get all PA on you - because you know they really are - because if you tell them too many times that their help isn't needed, they'll go away and pout and make life that much more difficult for you.
But the thing is, it's impossible to control what other people think, feel, or do. Or how they react. All you can do is control how you interact/react to them.
So, stop torturing yourself. Stop second-guessing what they're going to say or do. "Knowing FIL is a perfectionist and will comment on it, I tell him that DH needs a special tool to cut them diagonally. I never mentioned needing help sourcing the tool and indeed we had already made plans to source the tool on our own."
Don't guess what your FIL is going to say. You could be wrong. In your post, you mentioned that you proactively mentioned that your DH needs a special tool - then it turned out you mis-spoke and they ended up supplying you with the wrong one. So, they wasted their time, you got something you didn't need and can't use, and NOW you are in the awkward position of having to tell them all of this. (I imagine)
So, do yourself (and them!) a favor....don't volunteer that information. Tell them you've got the situation under control and DH will be finished with the project soon. Then, if they get critical because this, that or the other thing isn't up to their standards, this forum offers a lot of good techniques on deflecting the criticism - like beandipping, complete silence or using the "what an interesting assumption" phrase.
But I think the best way to handle it is to avoid the situation in the first place, if you can. Try to limit the information you give the in-laws about projects or other things that you believe they might be critical about. I know how it is. I don't think you're being too sensitive, but I do think you unintentionally give them the impression that their advice or help is both welcome and needed, and you do that partially because you think you know what they're going to say.
I say try to break that habit and give them the benefit of the doubt. They can be as critical as they want to be - it's still your house, your life, your business. Using the above techniques, over time, might help them break THEIR habit.
I'm so sorry you're going through this - I understand how annoying it is. I hope this helps!