Put her down, walk away, and completely ignore her when she does that.
Give her the message that bad behavior means no attention from you.
In my experience, that's how mama cats handle bad behavior from
kittens.

Listen to her. She's trying to tell you something ("put me down, I don't feel
safe here"). She has claws and teeth and could hurt you if she wanted to, but
she isn't hurting you. She loves you.

She is feeling afraid of (or angry at) the dog. She gets a little jumpy when
the dog is there. She feels a touch and goes to bite at it, sees it's you,
and pulls back. My Rowan used to do this - she doesn't much like my dog,
either.
Just put her down so she can go somewhere she feels safer or, better yet, let
her know you will protect her and make the dog go away when you're holding
your cat. Once she understands that you won't make her sit there while the
dog is close enough for her to be threatened, she'll lighten up.
NEVER force your cat to stay on your lap if the dog is close enough to make
her feel uncomfortable. If you've been doing that, that might be why she just
started this behavior.
Keep in mind that some cats will never really like the family dog. She may
hiss at the dog for the rest of their lives when she feels threatened.

My guess is misplaced aggression.  She directs it toward you instead of the
dog - you're more handy, even though the dog's the cause.

Or maybe a low saturation point - re: petting, due to the dog being in the
vicinity.  Have you ever been petting her when her tail starts to twitch, &
instead of liking the petting, she becomes ambivalent about it instead?
That's when she starts to hit her saturation point.  If you continue to pet
her, she may then scratch or bite.

As time goes by, she will probably become more tolerant of the dog.

Cathy