You can't have two different passwords for the same account. What you can do is either:
- Have a password to access the phone itself (as Al suggested); or
- Have a second account set on the phone, that has access (through sharing) to your main account calendar and contacts (I'm not sure how this works or even if it does, to be honest); or
- Have some VPN client on the phone, that gives you access to your home computer.
Yes, these are very looooong shots, but what you are asking for is not that simple (or even possible, for that matter).
What you can also do is setup the two-step verification, indeed. This way, you will have a special app password that allows it to connect to your account.
After you turn on 2-step verification, non-browser applications and devices that use your Google Account (such as the Gmail app on your phone or Outlook), will be unable to connect to your account. However, in a few steps, you can generate a special password called application-specific password to allow this application to connect to your account -- and don't worry, you'll only have to do this once for each device or application.
From this Accounts help page (emphasis by me).