SOO so sorry to hear about your daughter's diagnosis! It's good to know she is responding well to treatments.
Regarding the question in your OP - PERSONALLY, I'd stick with Kindle. First, I absolutely LOVE the kindle and Amazon, and have been so happy with the way Amazon has handled returns and exchanges for my family of a dozen or so Kindles (my mom, my MIL, my aunt, three of my sisters, several friends, kids of family and friends, etc.)... the other reason is because all the accessories you have (cords/plugs etc), should work with your new Kindle too; I have no ideas about other ereader plugs and cords. Also, you've probably already got quite a few books through Amazon, and it's going to be simple to transfer to a new Kindle - and simple is good, espeically when you have other more important distractions!
If I needed a new Kindle right now (my Kimy, a Kindle 3, is still working just fine thank you!), I'd probably buy a used on on eBay because the current Kindle and Kindle Paperwhite don't appear to have 3G! If I couldn't do that for a reasonable price, then I would buy the Paperwhite.
Regarding battery life - Amazon rates the battery life on the Paperwhite as TWICE that of the regular Kindle (You are not allowed to view links.
) at eight weeks! Having touch screen would be very nice too! But, if money is an issue, then I think you'd be perfectly happy with the standard Kindle at just $69 retail! I have a friend with the Paperwhite and she LOVES it.