Ah, sometimes I wonder why people ask what breed my dogs are. Because when I tell them that my big boys are yorkies they always look at me and say, "No way they are yorkies.. they must be mixed. Or perhaps they are silkies." No, really they are yorkies! It is like they don't believe me.. Then why ask!?
As for your neighbor though, maybe she was just using it as a conversation starter, or perhaps she just isn't really familiar with a lot of different dog breeds. Also, since there are so many mixed breeds out there now, maybe she wasn't sure if your dog was mixed too.
For your other question, I cannot help you because whenever my dogs see another dog, they want to run over and play with them too no matter how big they are. My Marshall is like your Tila because he squeals like crazy when he spots another dog and pulls really hard on the leash. Hopefully someone will have some experience with this on how to fix it.
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♪ Jimi | Marshall | Hendrix ♫
"When the power of love overcomes the love of power, the world shall know peace." - Hendrix