schrimer,
I have both (door and Crate) but, I have never used the Crate
for anything other than Transport. So, I'm a little weak on that point.
But, I have used Paper, and I put it right in front of the Doggy Door
when I didn't want the Door open. This way, one trains to get them
going to, or toward, the same location when they want to potty.
I'm going out on a limb here a little, but, IMHO Yorkies would very
much prefer to potty outside (mine do), so, just give them a chance
and I think they'll take it up on their own.
You might try it this way...
If you can close off the area where the Crate is, you can just leave
the door open on the Crate, put the paper down in front of the Doggy
Door, and see if that works for you.
My Crate, the Paper and Doggy Door, are all in the Utility Room,
and it has a door that can be closed to the rest of the house.
The door is open on the Crate, but, they never get in it, except
to attempt to hide a Treat from the other.
I disallow outside access at nights, and when we leave them at
home alone. However, in my case, both mine are very reliable
about the potty, and have complete access to the house all the time
whether we're home or out. Actually, that level of access is more
security related for me.
Good Luck !