How do I enter Recovery mode without keyboard or Home button?
The best way to get this done is to use Android Debug Bridge (adb).

Get Android SDK on your PC, plug in your Android Device, and run adb reboot recovery in ADB shell.

That command restarts an Android device in recovery mode.

Here is a lifehacker article that might be useful:

The Most Useful Things You Can Do with ADB and Fastboot on Android

And here is an extract:


  adb reboot recovery
  Function: Reboot your phone into recovery mode.
  
  A lot of functions like flashing ROMs to your phone require you to boot into recovery mode. Normally, this requires you to hold down a particular set of buttons on your phone for a certain length of time, which is obnoxious. This command allows you to boot directly into recovery mode without performing the complex finger dance of your people.


Hope this helps.



PS: this method was already recommended by a user (at the time of posting) named GiantTree as a comment. I am only posting this answer so that others might find this thread appropriate and useful.