Yes she was. Yes they did.
IMHO, The most plausable explaination is it was done because the family was pressured. "Your poor daughter will be a pathologist's plaything. Every time someone questions what happened, they'll have her disintered and cut up. She'll never really rest in peace..."
Why? Again IMHO, being able to establish she was pregnant and Teddy was the father, provides a plausable motive.
As she was a Catholic, an abortion was out of the question. Having an illegitimate child had sufficent stigma to end a political career.
This moves it from probable accident to possible murder.
But, I could be wrong in my belief.