I'm also going off memory, but something tells me that woman is Clara and
not Isabel Lyon.

The setting is Connecticut on a day where dining outdoors would be
comfortable.  I presume, without any evidence, that the film of Mark Twain
walking around the house and standing in the doorway was taken on the same
day as the dining film.  That day seems to have been a day of very clement
weather.

I think, if I remember correctly, that Twain fired Lyon in March of 1909,
possibly in April.  I think Jean may have come to live with her father just
around the same time.  It seems unlikely to me that they would have dined
outside in March, or even early April, in Connecticut, although I suppose it
is possible.  I think it's more likely the film was made in the summer of
1909, and that Clara was there for the occasion.

There is something of a superficial resemblance between Clara and Miss Lyon,
although Lyon was an older woman.  That resemblance makes it hard to say for
sure who the person in the center of the shot is, but there is something in
the hairline that suggest Clara to me.  I don't know what.  This sort of
visual detective work is not made easier by the very low resolution of the
YouTube copy.  I'd really like to see a pristine digital copy if one is
available.

In fact, the only person in the video who I can honestly say I am confident
I know the identity of is Mark Twain, because he has a distinctive look
about him.  I believe the woman on the right of frame is Jean because she
has Jean's lean, athletic build and angular features like her mother's.  The
woman in the center just doesn't appear very well in the YouTube copy.
Whoever took the shot did some crummy composition work, putting the most
active person in the shot behind some sort of centerpiece.  Oh well.

Carl