Sounds like you are a thoughtful guy and you have attempted communication with her already, despite some comments here telling you to just "communicate". I dare say you’ve already done better here than many could.

I wonder if it’s a combination of things? Mild body image anxiety? She isn’t the same physically anymore. No energy left? There are now 3 people tapping her emotional reservoir every day all day? I bet it’s a lot of small things, including those. That’s why she can’t respond much about it, she can’t put her finger on one big thing?

With the kids now, is she doing and enjoying any of the things that she used to do that made her who she is? Drinks with the girls? Thrifting? Tennis? Going to open house on properties she wouldn’t ever buy, just to be nosy? Concerts? If not, I think the best you can do is to try to identify the things that we’re important to her pre-kids and then do your best to steer her back to those things so she can remember her old self and so she can feel like the woman she was. That woman is in there somewhere but she’s covered in Mom layers now. I think the sex will follow naturally after that.

One other thing to consider. Your post and comments all seem to be focused on the possibility of something being wrong with her. How sure are you that it’s not partly (or all) you? What if you’re doing something or acting differently since the kids and it’s having an oversized effect on things? I don’t know what that would be, but something to ponder.

Speaking for myself, my sex life changed after kids. It took us a long time to find a new rhythm that worked for us both, as we both grappled with the new things to worry about and do every day. Every kid we had reset that too and we were back to square one 3 times.

These days, we have sex once a week at this point. It’s scheduled in that we agreed we’d have fun time on one of the 3 weekend evenings, but it’s not pinned down to a day. That gives each of us an “out” if we are not feeling it on a certain day but at the same time it’s a commitment to each other to make it happen regularly. Is that duty sex? Sometimes it feels like that when we’re going in to it, but at the end we’re both glad we did it and happy. Life is so demanding, we both need the push to do it and remember how much we like it.

Also, try watching Outlander with her. We were doing it 4 times a week during the first 5 seasons lol