In ch. 16, Mrs. Dashwood remarks that they had been reading Hamlet with Willoughby, but had not finished it yet. I'm of the opinion that Jane Austen would not choose the name of a particular play by accident--why Hamlet out of all Shakespeare?

I like to amuse myself in wondering how far they got in their reading. Hamlet is dealing with the death of his father. You cannot get very far into the play (beyond the second scene) without encountering that topic.

I wonder how Marianne and her mother, especially, would have reacted to Gertrude questioning Hamlet about why he is still grieving so much for his father's death to which Hamlet replies:

'Tis not alone my inky cloak, good mother,
Nor customary suits of solemn black,
Nor windy suspiration of forced breath,
No, nor the fruitful river in the eye,
Nor the dejected 'havior of the visage,
Together with all forms, moods, shapes of grief,
That can denote me truly: these indeed seem,
For they are actions that a man might play:
But I have that within which passeth show;
These but the trappings and the suits of woe.

Would they have thought anything about the idea of putting on the 'trappings and the suits of woe'? Not to say that their grief was not genuine over Mr. Dashwood, but they also did put on a real show of it.

Or how might they react to this reply of Claudius'?

but to persever
In obstinate condolement [demonstrating grief] is a course
Of impious stubbornness; 'tis unmanly grief;
It shows a will most incorrect to heaven,
A heart unfortified, a mind impatient,
An understanding simple and unschool'd...

He's saying that to persist in demonstrating grief to such a degree shows a weakness of heart and mind, rather than the reverse. Of course they could dismiss his speech because he's a villain and because they wouldn't care about being unmanly, but there is certainly some irony there, at the very least, in imagining them reading or hearing those lines read.

I wonder if they got as far as some of the discussions between Ophelia and her father and brother?

How would the group react and think when Laertes says this to Ophelia?

For Hamlet and the trifling of his favour,
Hold it a fashion and a toy in blood,
A violet in the youth of primy nature,
Forward, not permanent, sweet, not lasting,
The perfume and suppliance of a minute; No more.
...
Perhaps he loves you now,
And now no soil nor cautel doth besmirch
The virtue of his will: but you must fear,
... his will is not his own;

I can imagine Marianne scoffing at someone being unable to tell the difference between a love that is forward, not permanent and sweet, not lasting, vs. the real thing.

Or, if they got this far in the play, they may have read aloud Polonius advising Ophelia:

'Tis told me, he hath very oft of late
Given private time to you; and you yourself
Have of your audience been most free and bounteous:
If it be so, as so 'tis put on me,
And that in way of caution, I must tell you,
You do not understand yourself so clearly
As it behoves my daughter and your honour.