Here is the family crest of the Irie clan. Itfs not a big clan so there is only one. The pattern of the three circles is very unusually lined up, and the pattern within the top circle symbolizes paving stones so they say. http://bit.ly/1fuCaU8
The main lineage of the Irie family derived from the Fujiwara clan (southern faction), and as Uco noted, its first appearance in the written record comes from Taiheiki, the 14th century war literature. By the mid-14th century during the Nanboku-cho era, the chief of the family re-established himself to the northern Osaka, and built the original Takatsuki Castle. The familyfs reign didnft last that long though, since they lost the war against Nobunaga Oda as the one of generals under the Daimyo Hosokawa in the mid-16th century. At this point, I suppose that the most of the Irie family became commoners (the gold medalist swimmer, Ryosuke Irie, is from Osaka), but some stayed as samurai and moved to Kumamoto and served for Daimyo Hosowaka from the early 17th century until the end of the samurai era. If your mother was from Kyusyu, she could be the member of this Irie family, who after the end of the samurai era, might moved onto Sasebo to find jobs.
Another possibility: Some of the Irie family under the Daimyo Hosokawa owned the land called Irie Village (doesnft exist anymore) in the modern day Kagawa prefecture. This Irie family moved to Goto Islands in Nagasaki prefecture (same as Sasebo) during the early 17th century and the family lived off as the local police/tax officers in the Fukue City area. Your family could be from here, maybe more so than any other places because even today, itfs typical for Goto islanders to move to Sasebo, Nagasaki, and Fukuoka in order to make livings other than fisheries. There is a direct ferry from Goto to Sasebo.
You have to understand that not all Japanese have family crests, and most farmers or artisans didnft have names until the end of the samurai era, and they simply adopted the name of the local leaders, or the name of places they were born. There is a large possibility that your family didnft have one, but as the history shown above, you could be the member of this Irie family if you can link yourself to Goto Islands, Kumamoto, Osaka, or Shizuoka area.