The problem with the connections is that we don't know enough. Are you watching all of this by hooking coax cables and tuning the TV to channel 3, or are you using video cables. In any case, the system has now become complex enough that you need to deal with source switching.
I am going to make an assumption that your signal path currently looks like this:
Satellite Receiver -> TIVO -> Television.
You connect everything with red, white and yellow a/v cables, or perhaps you use coax and channel 3 for part of the setup. You watch everything through the TIVO and never bypass it to watch satellite TV directly. If this isn't the case, we will need to start over.
The DVD Recorder needs to figure out where to get the signal from. By default it is probably using the television tuner that is built in. Given the current situation, that is probably the now useless NTSC tuner that used to be the standard. If so, we need to forget it and move on. If you ever want to record over the air signals, we will need to come back to this.
Your best bet is to get signals from the TIVO. Does the TIVO have two sets of outputs. Your message seemed to say that. In that case, hook the second output of the TIVO to the inputs of the DVD recorder, leaving the other TIVO outputs hooked to the TV. Now, connect audio and video outputs of the DVD recorder to a different input of the TV. You should have several to choose from. Now, in order to watch the DVD, you will need to select the input on the television that is connected to the DVD player. Try that out with a regular DVD and confirm that you have good audio and video.
Almost there.
Now, you need to use the input selector on the DVD to select the A/V input. That is done n a number of different ways, depending on the player. It may be an input selector, or it may be done by selecting a certain channel number. If you do it right, the TV should start showing what is on the TIVO. However, for some recorders, it may only show it when it is recording, which is why you need the second path from the TIVO to the receiver.
Give that a try. I hope this didn't just add to the confusion. Let us know how it works out.