Caroline Astor was an cousin not a descendant. She's descended from the Astor who fled to Britian because Caroline outshone him socially. Caroline Astor had one son, John Jacob, who went down on the Titanic. He had two sons, Vincent, from his first marriage, and John Jacob from his second. Rose is not a descendant of either of those two men, and thus is not a descendant of Caroline.
Her bloodline is no more impressive than many other British families, especially when you start to look at the families with the higher ranking titles, like the Devonshires, Spencers, Marlboroughs, etc.
The VCs are descended from old stock, stock even older than the Astors (and the Spencers, for that matter), but I guess since their ancestry is in Belgium, you choose to discount it?
Emilie raised her children the same way she was raised, and, considering what her father-in-law was like, probably in much the same way her husband was raised.
There are no titled families in Britain that could ignore a financial boost like the one they would get should Tamara inherit the entire Westminster fortune. None come close to what she'd inherit -- not even the Cadogans, Howard de Waldens, or the various Guinnesses. In fact, if you added up the worth of those three families, it's still not half of what the Westminsters are worth. So who are these "plenty of titled families who are exceptionally wealthy and could ignore a financial boost" you claim exist?
I can't understand someone who despises two young men they'll never meet and dismisses the intelligence of the two young women who chose to marry them.