In the second part of your question you seem to be worried about your notebook being stolen and, with it, your private-keys for your password-less SSH login to your servers.
Please note that this can easily be solved (the private keys issue) by storing private keys "encrypted" with a "passphrase": they can be encrypted initially, while generating with the ssh-keygen utility, by providing a passphrase at the end of the generation process or, if you already have them unencripted, using the ssh-keygen utility with
-p option. Once the key is encrypted, at every login you're asked to enter the related passphrase and.... if correct, everything will proceed normally.
Also, if you don't want to enter the passphrase every time you launch the ssh client, you can use the ssh-agent: it can keep track, in memory, of unencrypted private keys. You can simply run ssh-add pointing to the file holding the encrypted key and, after asking for the passphrase, the key is added to the set managed by the ssh-agent. Afterwards, every time the SSH client require a passphrase-protected key, the ssh-agent transparently provide the related unencrypted private-key to the ssh client. So, for you, it's not needed to enter it interactively.
Please note that ssh-agent can manage plenty of keys, and obviously you can "tune" your notebook/desktop to launch the
ssh-add utility (to populate the ssh-agent set of keys) at login/startup time.
Also, should someone steal your laptop, your private-keys are probably not the only "sensitive" content you're going to give out: please note that with today's Linux desktop distributions it's VERY easy to set-up a notebook relying on "encrypted" file system (the
/home as a starter, but the whole
/ if needed). So, please, consider this also.
All of the above, obviously, does NOT apply if you DON'T rely on YOUR OWN notebook.
P.S.: as for your possibility to store the two halves of the unencrypted private key on different mediums: I strongly advice you not to do this, as maintaining the two pieces of sensitive content in an unencrypted form is much, much worse, than keeping two full copies of the whole content, encrypted!