I understand that you want to know which Slingbox model to get in order to avoid any conflict with the home viewers or Slingbox remote users.
First, if your son and daughter are going to use the Slingbox, you must have in mind that the Slingbox will allow only one connection at the time. This means that if you are using the remote connection to your Slingbox no one else will be able to watch it at the same time.
No, regarding the main question your best option is to get the Slingbox PRO-HD. Among its features, you can take advantage of the internal tuner. This feature will allow you to "split" the signal without affecting home viewers.
You will need to connect a splitter on the coaxial cable that comes from the wall. Then, from the splitter you will send two lines out: one to your cable box or DVR and the second one will feed the Slingbox. This way, you will be able to get the TV signal.
The only disadvantage is that this setup will allow you to get only the basic cable service channels. As a second option, you can also get a secondary set top box. This way, you can dedicate this specific unit to work with your Slingbox. The following link will allow you to get all the information about the Slingbox PRO-HD: