is really quite easy.
Inside your Picture folder there is a folder called iPhoto Library. It contains all your pictures. To ensure that ALL your pictures are in the library, you can "consolidate Library" but this only applies to older versions of iPhoto.
You should never just drag pictures into iPhoto, you should always use the Import option from the menu bar to ensure that everything is in the Libary.

On NO account should you attempt to edit the contents of the iPhoto Library. Do NOT mess with it.

To move your iPhoto library to another drive, Quit iPhoto and copy the ENTIRE iPhoto Library to its new location. Just pick up the iPhoto Library and drag it to where you want it to go.
Launch iPhoto while holding down the Option key and when the dialog box appears, navigate to the new location of the iPhoto Library.
Once you are happy that you have all your pictures there, you can safely trash the OLD iPhoto Library that is on your internal HD. Just drag the ENTIRE library to the trash. (See the warning below)

IPhoto will always open the last library used.

WARNING
On the subject of that external drive. Did you format the drive as HFS+(Journaled) before you started to use it?
If not, make sure that is NOT formatted as FAT16 or FAT32. This is the normal format scheme used to ensure that the end user can use the drive straight out of the box.
The format is flaky and files over 2GB do not behave at all well.
Format the drive to HFS+(Journaled) at the earliest opportunity, if you have not already done so.

ADVICE.
WIth a library of over 10,000 photos, one would seriously hope that you have already taken steps to ensure that you have a COMPLETE backup of them.
One hard drive crash, and they do happen, will reduce ALL those photo's to just a distant memory.

P