Translation:How is your uncle in Tokyo?
In that specific case, the mother would almost always say just "uncle", "your uncle" or "Uncle (name)". Neither mother nor child would be likely to say "the uncle" or "an uncle"; this phrasing would have to be either a joke or referring to the concept of an uncle. Similarly, if speaking about the mother's father, both are likely to call him grandfather, using the child's frame of reference. If the mother was speaking to her husband, however, she would be far more likely to refer to these people as her brother and her father, but this varies by the individual, their age, their family, and where they live.
But if talking about your uncle in Tokyo, I would always say "your uncle in Tokyo" rather than just "uncle in Tokyo" even if it is not possible that I have an uncle in Tokyo. In Japanese, does the phrase 「東京のおじさんはお元気ですか」 always refer to your uncle in Tokyo, or could it be my uncle in Tokyo? Is there any way to tell besides context?
I remembered that you call him by 'name' instead of saying uncle. Different from you, especialiy children don't call adults by their personal name. We call my uncle to 'おじさん'. I don't know this sentence's context. But this sentence is natural. Because in the relatives, many people has the same surname. Because they are originaly one family as sisters and brothers. Therefore we add some words for distinguish them. If you have two uncles who live in Tokyo, you call the town's name instead of Tokyo, maybe.
'The child's frame of reference', I think that this is the same.