I was in essentially the same boat. My phone (Droid BIonic, unlimited 4G), moms phone (flip phone). Here is what I did (and which has worked so far).
1. Upgraded the dumbphone and bought the LG G2 on Verizon wireless using the coupon (verizon30) and put it on the dumbphone line. Turned it on and activate it so that it worked on the dumbphone line.
2. Called Verizon, asked them to re-activiate the dumbphone on the LG G2 line (I had to call verizon because I was not able to do this online for some reason).
3. Once I was sure that the dumbphone was re-activated, I then went and activated the LG G2 on my unlimited line via the website. I did not have to swap out SIM cards between my LG G2 and my Bionic (and actually this would have been impossible to do since they are 2 different sized sim cards). Instead, there is an option on the website that allows you to type in the sim card #. When you get to this step, just enter the # of the LG G2 sim card, and NOT your existing sim card on your Galaxy s4.
Now I have the LG G2 active on my unlimited line, and my mom has her dumbphone active again. My Verizon website still shows me as unlimited 4G, and it shows that she has no data on her line.
The only caveat is I don't know how the bill at the end of this month will account for all these changes. From what I understand, I will be charged the pro-rated amount for the data I used on my mom's line (which should be about $1). I really hope they don't hit me with any phantom charges, but that remains to be seen.