Re: bathrub/ floor trouble
My bet is that when the tub was installed it was not bedded in mortar to support the bottom of the tub fully, hence the extreme amounts of flex you are seeing.
A retrofit fix will be tough, but not impossible. Basically what you need to do is gain access to the underside of the tub and force mortar under the bottom of it to take up any gap. When cured, the mortar should prevent the tub from flexing as much.
Another option would be to switch to a beutyl caulk that stays extremely pliable that can handle the stretching and pulling.
I suffer from CDO ... Its like OCD, but in alphabetical order, LIKE IT SHOULD BE!!!