Lots of healthy and adorable Yorkies have ears that don't stand up. In fact, vets often tape Yorkie ears up to train them to stand on their own. I've seen that technique work more than once in the short time I've been on Yorkietalk. Other times, as SoCal points out, they stand up on their own. Talk to your vet. As for runny eyes, that is common too. Some people swear that the hair around the tear ducts can be trimmed, and that takes care of the problem. Talk to a groomer about that.
It's easy to panic over these adorable little creatures, but they are remarkably tough. It sounds like your mom has a great little dog there that she will love for years and years to come.
Good luck, and keep in touch. Oh, and there's like a law that you have to post pictures.
Edit: Oops, Snow Yorkies posted as I was writing my note. Listen to her. She's much smarter than me.
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Mike ~ Doting Dad to Jillie, Harper, Molly, Cooper, Eddie (RIP), Lucy (RIP), Rusty (RIP) and Jack (RIP).
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