Perhaps your child isn't reading yet or is falling behind in math, there's a bunch of people just waiting to call you a colossal failure. "I told you this isn't going to work!" These problems would of course arise in a public school and also probably even worse, but that doesn't matter, because your spouse or in-laws are feeling particularly knowledgeable about this subject. Everyone knows what's best!
The good news is you're not alone! This is one of the most common problems homeschooling parents have. Outside pressure. People think what other people do is the safe thing to do. If a hundred people ran out of a building I would also assume it's on fire or something and not enter. In this case, however, you're the one that knows best. Who's the closest to the child? Who actually did teach them for the last year? Who is most likely to help with whatever problem they have now?
There are no easy solutions here. However, I would suggest making an effort to get the critical family member to teach a few lessons. Leave the axe at the door though. You want to approach casually. Ask what did they like about school when they were young. What subjects did they do well at? Only once you see the sparkle in their eye about a subject you can pop the big question - "Would you like to teach that"? The subject doesn't have to be academic. If you figure out what they do at work all day, they can perhaps teach one part of some activity. Maybe it's computer stuff, like Excel? Maybe it's gardening? Cooking? Doesn't really matter as long as they put some effort in and feel the responsibility.
Getting them involved is the best cure for criticism because then they're also responsible. They would probably conclude pretty fast that the child is smart and does things in their own way. So do you. Even if they don't teach, then at least
If what your child is struggling with is reading, then you may want to take the 3 steps to help kids fall in love with reading, try more general tips, or perhaps check for medical issues. In any case, if you're on the verge of giving up read this first.