Maybe this will help.
Several years ago, the AMHR reg was an open registry. If you had a horse under 38" you could reg it for like $30.00, regardless of the age. This was happening when I first started with the minis 10 years ago. That is why you can find horses with completely un-know in their pedigrees.
Now, people with ASPC horses, reg their 38" & under shetlands into the AMHR. Now, they had double reg. horses. These days, if a Shetland stays under 38" at three, they can be hardshipped. You can not hardship into the ASPC at all.
Now, if you cross two double reg horses, ASPC/AMHR the foal is double reg. If one parent is ASPC/AMHR and the other is only ASPC or AMHR, the foal is reg in the same reg as the single horse.
ASPC/AMHR + ASPC/AMHR=ASPC/AMHR
ASPC/AMHR + ASPC=ASPC
ASPC/AMHR + AMHR=AMHR
However if the ASPC foals stays under 38" at three, it can be hardshipped.
Here is an exsample of an AMHR horse by an AMHR stallion and out of an ASPC/AMHR mare
Dream Weaver's Midnight Serenade
His sire is 31", his dam is 38" and he is 36".
Hope that helps!