Linksys makes a HPNA->Ethernet bridge for about $99. You need one to make this all work.
Dual line makes no difference, as long as the phone jack in your sister's room and the one in your father's room have a telephone number in common. You'll need to use a splitter to convert the dual line jack into 2 single line jacks, then figure out which one corresponds to the number in your sister's room. Then you'll have to use a combination of splitters to put the 2 lines back into a single jack to connect into (I assume) your dad's 2-line phone.
Here's an attempt at a picture (edit - didn't work too well

):
2 lines --> splitter --> line 1 --> HPNA card --> splitter --> dad's 2 line phone
line 2 just goes from the first splitter to the second splitter.
You can use the phone and the network at the same time, no problem. The speed is pretty good, not quite equal to 10mbps ethernet but plenty good for sharing an internet connection or printer.