If you know the actual copyright holder, I suggest you contact her again to see if she can explain the other shop owner's copyright claims.
Or you can ask the other shop owner for her copyright registration number. She does not necessarily NEED to have her copyright registered - copyrights are automatic upon creation of an original/creation work - but if she does have a registered copyright, that will show exactly what it is she is claiming rights to.
Have your felt horse binkys been removed from your etsy store, through a DMCA takedown, or did you remove the items on your own, after notification from the other shop owner?
Because it is difficult to tell what is going on, you might have to have the items and the facts personally reviewed by an attorney in your area - but from what you have written here, I do not see that the other shop owner has any legal right to prevent you from selling the horse binkys.
The shop owner's website page is copyrightable, as a note. Perhaps that is what is indicated on her site?
One additional note: Anyone can purchase a copyrighted item and resell it, under the First Sale Doctrine. So selling felt horses that you purchased, or clips that you purchase, or pacifiers that you purchase, is not a problem. Anyone who purchases them can resell them (or give them away or throw them away). Where the copyright permission requirement comes into play would be in selling altered or modified versions of the original copyrighted work. That is creating a derivative work, and that is one of the exclusive rights held by the copyright holder.