I'm new here, so maybe you've already tried this (for years), but how about:
She: I'm tired.
You: Yeah, you have an awful lot to do around here. It must feel overwhelming for you.
She: Yeah, sometimes does.
You: What's that like for you?
She: (startled and suspicious) What do you mean, 'what's it like?'
You: I want to understand how it feels for you in this R when you feel overwhelmed. I really want to understand and listen to you.
She: (still suspicious) Well, I feel like I'm responsible for so much. That all the things that need to happen won't happen unless I stay on duty all the time. (loosening up a bit) And, you know, it's funny. It's not even the stuff that needs 'doing' as much as it is the mental exhaustion of always having it lurking in the back of your mind. It's really like being mentally on duty 24/7. (wondering if she's said too much and now you'll start telling her how to 'fix' herself and the situation... she withdraws a bit)
You: Yeah, I get that. (but you surprise her!) You know, when we were kids, we used to worry about homework, and pimples, and was that guy or gal that we liked ever going to call us-- we thought we had SOOO much on our minds. Now, just being a grown-up is so damn hard... and being a parent on top of that! Just making sure everyone is safe, fed, sheltered, healthy, happy-- God, it would be great to just get out from under every now and then. But even on vacation-- we're still the grown-ups! Safe, fed, healthy, and happy-- we even have to deliver that to the kids on OUR days off! It sometimes just seems to be too much... (pregnant pause... let it go on for as long as necessary)
She: I wish I didn't feel so tired all the time. I want to have fun, too, but I seem to have forgotten how. If I relax my vigilance for even a minute, then I get behind on something or other that needs doing. (she's testing you to see if you're going to offer solutions...don't take the bait)
You: Let's think about that and talk about it again sometime soon. We're in this together. I know it sometimes may not feel that way, but it's you and me. (end of convo for now)
Maybe on another occasion: She: I know I could delegate more to the kids, but (choose one) a) they have so much to do anyway. Being a kid is not like when we were kids. They have so much homework and extracurricular things, and there's already so much pressure on them. I want them to be kids while they still can; or b) I feel like I'm shirking when I delegate too much. It's my responsibility to do certain things; or c) my parents didn't give me chores to do, so I just don't feel comfortable with that; or d) my parents gave me a billion chores to do, so I'm not comfortable with that.
The thing about you listening to her and not offering solutions AT ALL is that if she talks enough, she might get to the bottom of why she's really tired all the time... and it may be something surprising... and something that CAN easily be fixed.
I'm positive she doesn't do it just to piss you off... well, I'm fairly certain of that.
I know that feeling of being On Duty all the time-- my late husband was disabled throughout our marriage, and I used to be mentally exhausted ALL OF THE TIME. The only other emotion that crept in was anger at the situation. Yes, I loved him... BUT... it was very hard...
I question whether 'calling her on her stuff' will ever be effective. It just makes the other person defensive, and then your excellent point is lost in the heat of battle.