Next time she asks you, say, simply and pleasantly,
I'm sorry, I can't help with that.
You're done. You don't need to explain why. This is a polite and acceptable response to almost any request. ("Help! my baby is stuck in that burning building!" deserves more, but "please help with that chore I said I would do" does not.)
Should she ask why, you are not obliged to answer. There are several phrases that indicate you are not going to provide an explanation. "It's a long story" is a polite one. So is "I simply can't." Try not to wobble further than "I don't want to list all our reasons, I am telling you that I will not be able to help with that." As I am sure you know, listing reasons is giving the person something to contradict and argue with. You don't need that.
Should she push you, "Oh, come on, surely you can, it's nothing for a strapping young thing like you! And you have a husband who could help too!" you just repeat your original demur: I'm sorry, I can't help with that. (Try to avoid "but" in this sentence, it is both stronger and more friendly without it.)
If you would be fine doing the task on your own, without her supervision and I guess without her getting the community praise, then you could consider making that offer, but I probably wouldn't. You two already don't like each other and this seems like it would give you something to bicker about. Focus on being a sympathetic neighbor who is sorry to hear she can't do that thing after all. Do not get caught up in "well who is going to do it then" or any of that drama. Smile a lot. You have no reason not to smile.
She may give you all kinds of explanations about why she can't do it. Agree with them. "Yes, I can see, the bending would be too much for you. It's a shame." Do not take them as prompts that mean you should do them. She may give you a speech about how important the chore is. Agree with those too. "Yes, it's very important. That's why I was so pleased when you volunteered to do it. Like you, I think it's a real pity that you can't do it." Pleasant, friendly, no argument at all. Complete agreement.
I have had my share of people in my life who try to get me to do something by hinting and nudging and telling me it's really hard for them and wondering if there was any way I could help a little and hinting some more. I have found that the best way to deal with them is to respond to the literal surface meaning of what they said "I can't do it", "It really needs to be done", "I wish someone could help me" and not to the subtext "so you should do it" -- arguing with an unsaid subtext is very very difficult. Life gets easier when you politely and warmly respond to what is literally said. There is quite simply no argument happening. "I can't do it." "I know, what a pity."