Well, I don't see any problem with sharing your books with family members.
Amazon actually allows you to link your Kindle account with
one other account via the Family Library setting.
calibre can be used to run a
Content Server, although in order to access it outside your local WiFi network you will need to set up port forwarding on your router and use a service like
DuckDNS.
Also, set a password from within calibre to prevent unauthorized access by non-family -- e.g. random people on the internet pinging random servers and discovering your library.
You will also want to DeDRM your library -- see
https://apprenticealf.wordpress.com
Sharing your calibre library with your sister doesn't help much if the books are DRMed to your Kindle (and Kindles use per-device DRM, not even per-account).
P.S. Step
away from iBooks. Now.
There is no way to access your iBooks purchases on anything other than an
iThing logged into
your Apple ID.
All the serious ebook readers avoid the iBooks store like the plague.
