Okay. Quasimodo apparently still existed in some storage.
This was all quite confusing since the methods of Saddle and MyPet are rather different.
Thus the key steps are:
Vanilla: Use a saddle, and right clicks for taming and mounting and using a lead
MyPet: have a lead in inventory or the task bar:
(1) get a lead (instead of a saddle)
(2) click left instead of right: this is taming it
NB 1. Without a lead you are hitting the horse
NB 2. If the horse already has a saddle, then clicking left with a lead is also hitting it.
Thus do not combine the vanilla saddle with MyPet
(3) click right with the lead to mount, shift to unmount (retrieve the lead)
(4) use /petstore and /pswitch for storing and unstoring
(5) keep the lead in your inventory for such events (instead of a saddle on the horse)
(6) riding a horse in this manner means that e for the inventory doesn’t work anymore when you are mounted, so use /petinventory
(7) when you tp, then the horse will not come with you, but you must /petcall and remount again
(8) use /petname (because nametags can be lost with /petrelease)
(9) the horse is following you around, unless you tp. Give /petsendaway otherwise.
(10) do not use the lead with a left click on a pet owned by another player, since the lead will disappear.
(11) beware that /petrelease means that others can claim the horse again, because it is no longer protected by either MyPet or a saddle.
(12) Accept that you cannot use a lead on a MyPet horse again, because right-clicking means mounting it.
Okido. Thank you all.