We used to have a portable for years. It was an off-brand 7" cheapie, and worked great for years. I've recently started looking again --- for the same reasons as you. I've seen 9" Sony at Costco for ~$99. They also have a 10" Sylvania -- which comes with carrying bag/case, headphones, etc for $99. I'd probably pick it.
For power, most all come with AC & DC adapters, so you should be good there.
For sound, you'll just need a 1/8" male-to-male. Plug 1 end into your headphone out on DVD player, and the other into your OE head unit. Select Aux In
on your display. Or, you can make them wear headphones while you and Grandma listen to your music
For mounting, you have several options. Many bags/cases come with straps to hang between the front seats (straps go around headrests). When we had ours, we simply sat it on the center console (in a bag/case), and put the strap of the case underneath the console lid. You might want to measure how much room you have to work with -- as some of the new portables get quite large.