Yukari Yakumo, Ran Yakumo, and Chen make up the Yakumo family. Chen is Ran's shikigami, and Ran is Yukari's. A shikigami is created through a technique that strengthens a beast youkai and controls it. The greater youkai Yukari converted a nine-tailed fox youkai into her shikigami, Ran Yakumo. In the outside world, you might describe this as something similar to installing software (the shikigami) into a computer (the beast youkai).
A beast youkai is an animal that has gained too much power and knowledge. It is unclear how these three youkai usually spend their days. One theory is that they quietly live together under the same roof.
Ran's job as Yukari's shikigami is to stay by her side and do whatever is required of her. Ran's shikigami, Chen, is always at Ran's side. Ran must be very busy with all that Yukari commands her to do, but she trusts Yukari and dotes on Chen. She does not consider her many duties a hardship.
Yukari Yakumo's estate is rumored to be the legendary stray house Mayohiga mentioned in The Tale of Tono. While the truth is unknown, these three youkai are probably relaxing in a house like this. It would have a warm porch, inviting the lazy drowsiness of frolicking cats... It would probably be quite a pleasant place.
Ran is a nine-tailed fox, one of the strongest of all beast youkai. For Yukari to be able to make a nine-tailed fox her shikigami and control her is proof that she is one of the strongest youkai in Gensokyo. It's clear that Yukari has an incredible amount of power within her. Ran herself has a shikigami named Chen, who is a cat beast youkai in the form of a black nekomata. It is incredibly difficult to control a shikigami who is powerful enough to have their own shikigami, which just goes to show how capable Yukari Yakumo really is.