... I know that Tyvek is used ALL the time to wrap up homes but NOT on the floor or ceiling sides.
Your sister is right, well, at least her sources are to say the least. By laying at least 6 mil thick poly plastic, you keep the moisture 'down' under the plastic. You need to put some 'weight' along the perimeter too to keep the edges down. (Usually, some bricks are used.)
I know what your thinking is on this but you may do more damage than good. Tyvek does allow small water molecules and air through the barrier. And if it gets through your barrier, you 'trap' it, thus, exacerbating the problem. The 6 mil poly WON'T let water through.
What I'd do is lay down the poly. Then, add in new insulation. When you lay up the new insulation, you can tack chicken wire up under the joists to hold up the insulation. (I prefer to tack up small nails and run string 'back and forth' to hold up the insulation.) THis way, if a joist-bay has a problem, or whatever, I cut the string that allows me the necessary access, then I tie it off, then I re-string the accessed area when I'm finished. (The chicken wire is nice but you have a lot more cutting to do.)
IF you have standing water in your crawlspace, that's a different problem. You still lay in the poly but you add a sump pump and pit at the lowest point. (This is another matter so I won't get into it unless you need this info.) Give the poly a try first. (Overlap it about 12") My best to ya and hope this helps.