JRace and Steve. Thanks for the help. Useful info.
For now I will stick with TeamViewer. I need to keep it working because I get remote tech support for upgrading and trouble shooting. If I get ambitious (or brave) I could add the no-internet options. I have a way of mucking things up. I gave up on LogMeIn.

JRace, You wrote: "Teamviewer will do both "Touch Enabled" and "mouse gestures"
you can switch from one to the other by bringing up the control panel (on the bottom of the screen)."
Is this for computers or the iPad app? I can't check it out now because I removed TV from my iPad after it messed up my music server. And I do not currently have a touch-screen computer.