another vote for “she” is correct, but both sound weird, and I would say:
Yeah, I would reduce it even further to something like “If anything needs to be done when you get home, she’ll do it” or “she can do it.” Or you could stick with the “that needs doing” construction, but that’s a little odd to me, too, even though “to be done” is more wordy. Not sure why.
Yeah, that’s the simplest rewording, and probably the best. But it doesn’t have quite the same nuance as the OP’s, which focuses the attention on who can do it rather than that it can, in fact, be done by someone.
Then I propose:
If there is anything that needs to be done when you get home, she’s the one who can do it.
Though I’d probably replace “do” with “handle,” given the context.
As for the OP: I agree “she” is correct, but that “her” sounds better. Emphasizing “she” sounds weird in that position (after a “be” verb).
Another variation:
If there is anything that needs doing when you get home, let her do it.
Sure, but English language doesn’t always optimise itself by seeking the most precisely grammatically correct form; rewording for greater straightforwardness and flow is not a glitch - it’s a feature. We’ll often prefer to say something less precise, less-awkward - even if we have to repeat iterations of the thing that when taken together, together clarify the intent
Assuming the intent here was that the ‘she’ in the subject has both capability and responsibility to do the thing, I think it would be pretty common for an English speaker to replace that awkward sentence with maybe something like:
“When you get home, if anything needs doing, she can do it; it’s her responsibility”
What’s also missng is that there is a bit of colloquial English here - we have an “if…then” construct, but omit the “…then…” and replace it with a comma.
If there is anything that needs doing when you get home then it can be she that does it.
Which would be more natural as…
If there is anything that needs doing when you get home then she can do it.
Although your original wording suggests the daughter might not be as cooperative or active, so it’s less definite.
If there is anything that needs doing when you get home then she could do it.
IOW …
If there’s anything needs doin’ when I get home it ain’t happening.
.