Where is Arwen's mum? Is Elrond a widower?

Celebrian is Arwen's mother and when I start to explain the history it gets confusing... but here it goes... Celebrian is the daughter of Celeborn and Galadriel. She married
Elrond in 109 Third Age and they were gifted with three children, the twins Elladan and Elrohir in 130 Third Age and then Arwen Undomiel in 241 Third Age. Celebrian was captured by the orcs and was captured and tortured. The twins rescued her and Elrond healed her, but mentally she was no longer very happy. So she passed into the Grey Havens which is near the River Luhn and then later out to sea. It's sort of confusing, so I suppose she did "pass away," but elves never really die, so in another sense she just left. I hope I didn't like totally confuse you.

zelo is absolutely right

Elrond's wife Celebrian (daughter of Celeborn & Galadriel) and mother to Arwen and her older brothers Elladan and Elrohir, is in Valinor (the Undying Lands).

She and her party (on their way to Lothlórien) were attacked by orcs. She was tortured by them, but she was eventually rescued by her sons. She was healed physically by her husband, but she could not fully recover in middle earth, so she took the ship to the undying lands to fully recover from her horrible experience.
So no Elrond is NOT a widower, for he reunited with her when he sailed.