This is "Last Contact" by Stephen Baxter. It was posted online for a time when it was nominated for awards... you can still find a web archive of that posting linked to the Wikipedia page.
Going point by point:
A female scientist has calculated the exact moment some wave of destruction, most likely the Big Rip, will hit earth. She's awaiting that moment together with her mother.
“Mum, it’s October.” Caitlin blurted that out. She looked thin, pale, and tense, a real office worker, but then Maureen had always thought that about her daughter, that she worked too hard. Now she was thirty-five, and her moderately pretty face was lined at the eyes and around her mouth, the first wistful signs of age. “October 14th, at about four in the afternoon. I say ‘about.’ I could give you the time down to the attosecond if you wanted.”
The story is a set of encounters with her mother over the time period from about when it's first announced that the universe is ending, to the moment Earth ends. Later in the story, she does spend the exact moment with her mother.
A probe has been constructed that might survive, but humanity will not, so there will be no-one to read out the data.
Yes, there are scientists investigating the phenomenon to the last moment, even if the data will be useless:
Caitlin looked at her curiously, but didn’t pursue it. “Listen, Mum. Some of us are going to try to do something. You understand that the Rip works down the scales, so that larger structures break up first. The galaxy, then the solar system, then planets like Earth. And then the human body.”
Maureen considered. “So people will outlive the Earth.”
“Well, they could. For maybe about thirty minutes, until atomic structures get pulled apart. There’s talk of establishing a sort of shelter in Oxford that could survive the end of the Earth. Like a submarine, I suppose. And if you wore a pressure suit you might last a bit longer even than that. The design goal is to make it through to the last microsecond. You could gather another thirty minutes of data that way. They’ve asked me to go in there.”
And indeed, at the end, a very faint hope that they have a probe that might capture data that will outlast the phenomenon and persist for whoever comes after.
And as for...
Her partner has committed suicide, since he (like many other people) doesn't want to witness the destruction.
This also seems to match:
"So how’s Bill and the kids?”
“We had an early Christmas,” Caitlin said. “They’ll both miss their birthdays, but we didn’t think they should be cheated out of Christmas too. We did it all this morning. Stockings, a tree, the decorations and the lights down from the loft, presents, the lot. And then we had a big lunch. I couldn’t find a turkey but I’d been saving a chicken. After lunch the kids went for their nap. Bill put their pills in their lemonade.”
Maureen knew she meant the little blue pills the NHS had given out to every household.
“Bill lay down with them. He said he was going to wait with them until he was sure—you know. That they wouldn’t wake up, and be distressed. Then he was going to take his own pill.”