I train my puppy totally off-leash outside / but since Sherryh - its not even your pup...I will adjust my opinion method some.
mmctag hit the nail on the head..."Leaving her outside is rewarding" / more so than, going into the house, and directly in crate lockup.
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I would put a 20 ft thin nylon rope on the pups collar and let it drag the rope, while outside.
Still play ball etc...all fun stuff.
On the COME command, use it when your at the end of the rope, holding it on the ground...with the bottom, of your shoe.
If the 6 month/old pup ignores the command...for even a second / real in the nylon rope.
Never let it disobey the human voice...avoid bad habits, getting more ingrained than good behavior.
Sherryh - your trying your very best, for the pup...while the friend/dogs owner, cares far less...by the sounds of it. (not a typical win-win situation / pup deserves more attention...you can't do it all)
So when your not their, the pups foundation (mental stimulation)...is probably way too limited & life is often real boring / for this smart pup.
[I believe in building eye focus/bonding & pup intelligence...thru. much play stimulation learning / over just plain walk exercise...with no true desire to always please the human caregiver]
The pup has already made the true cause/effect - if I come in the house, straight to the cage I'm going.
Should be a ball fetch or tug play inside, for 5 minutes first / before the dog is ever crate confined - avoid the existing cause/effect, that now exists.
Some dogs don't like cages, never will...I put our cage away for good, once a pup can be totally trusted.
But Amy always followed me inside - as I talked (up a storm) & communicated repeatedly, in a happy/most exciting voice...she still hated her crate though, always did & always would.