Should I redo my house wrap that is under the sheathing?
I can’t imagine that James Hardie will condone the installation of two exterior house wraps (James Hardie calls it : “Weather Barrier”) sandwiching the existing wall sheathing.
The existing sheathing will have moisture in it and probably large amounts of dryrot.
However, you want to install their product, their way, in order to protect the warranty. That’s why it’s important that you have an on-site inspection performed by James Hardie. Make sure you get his report in writing.
https://www.jameshardiepros.com/products/hardiewrap-weather-barriers
Btw, I would not use “Tyvek” or some random caulk. I would use only James Hardie products installed exactly how they recommended. (This includes NOT caulking above windows. This drives every installer crazy, but is required by James Hardie.)