But she did sign, yet was still incarcerated.

Technically, no. She wasn't incarcerated - she was detained. Incarceration normally refers to a term of confinement imposed for a criminal violation. Detention is her being confined to a particular area due to not being legally permitted to be at liberty in the country.

She signed, but the document almost certainly did not obligate the government to any particular time frame to take the steps of arranging for her transport out of the country. Again, we don't know the details - but it probably said that she agreed to remain in ICE custody until the government provided her transport home. That was always going to happen on the government's schedule at the government's convenience, and the most likely reasons that it didn't happen quickly are that: i) the shutdown through a monkey wrench into almost everything the government was doing; or ii) ICE is also up to their eyeballs in alligators because they are (wrongfully) trying to arrest and detain vastly more people than they have the capacity to properly handle.

Again, I can't imagine she's got a case after signing whatever document the government drafted. I'd be extremely surprised if it didn't contain so many waivers and admissions that they basically had the right to do whatever they wanted to her once she and her husband signed. Not legal advice, but signing anything the government LEO's prepare without having it reviewed by your own lawyer is likely to put you in a difficult spot.