Sadgranddad:
In addition to using a silicon caulk remover, make use of some abrasive finely ground powder, like pure Portland cement, or cement based floor leveler or even probably any good quality baking flour.
You see...
Silicon caulk removers don't dissolve silicon caulk... they just make it swell up and get soft so that you can remove it more easily by mechanical means such as scraping and scrubbing.
So, after using a silicon caulk remover, sprinkle some abrasive powder onto the area you're trying to remove that silicon caulk from, and rub that abrasive powder in with your finger.
If there is any soft swollen silicon caulk present, the powder will become embedded in it and reveal it's location by the grey (or whatever colour your abrasive powder is) discolouration evident on the surface you're removing the caulk from.
If there is NO soft swollen silicon caulk left on the surface you're using silicon caulk remover to remove silicon caulk from, then that abrasive powder will wipe cleanly off that surface, proving to both you and the world that there is no residual silicon caulk on that darn surface.
And, whatever surface still has residual silicon caulk on it (as evidenced by the fact that an abrasive powder will become embedded in that caulk), then you can then devote your efforts to removing that residual silicon caulk from the areas where the abrasive powder sticks to rather than those areas where it wipes off cleanly (proving there is no residual silicon caulk in those areas).
By using an abrasive powder along with a silicon caulk remover, you can identify the areas where you were not successful in removing all of the old silicon caulk, and concentrate on those areas.
Once you concentrate on those areas, and use the abrasive powder trick to confirm that ALL of the old silicon caulk has been removed from the surface of a tub or tile, the the new silicon caulk will stick like chewing gum to the underside of a church pew!
It's primarily the fact that most people are unable to remove all the old silicon caulk that causes their difficulties in getting new silicon caulk to stick well where it should.
By recognizing that silicon caulk remover causes old silicon caulk to swell up and get soft, and by using an abrasive powder to reveal the locations of that soft, swollen residual silicon caulk, you should be able to locate and remove ALL of the old silicon caulk.
And, THAT is the trick to getting new silicon caulk to stick tenaciously to tub and tile. NOTHING sticks to old silicon caulk, not even new silicon caulk.