That's why the advice to let the DH deal with it or the feeling that its DH's friend it's his job to sort it out don't work in this situation.
Your DH needs to start listening to you and your DD and not just allowing people to treat you like this.
Who are DD's parents? BOTH of you. But he let you take the flack. Is he not also responsible for DD? How much flack did he get.
You stayed at her house and thought Her house Her rules. She DID NOT pay you the same courtesy.
I did speak up multiple times but she didn’t take my comments on board.
She literally ignored you in your own home and undermined your parenting. From your posts, you seem to have clear ideas on parenting and managing your DD.
I disagree that other people can chip in as they like - particularly when there is a drip feed of criticism about completely trivial things. She didn't say things in a kind or positive way a lot of her comments just sounded very unkind. The one about not wanting to hold DD's proffered hand - what a cow.
You know what your gut reaction was to her behaviour. To the tone of her comments, over trivial things. Don't let DH join in with it and back HER up because he wants to be popular and approved of by his shit friend. People who let others do that because they are scared of being "confrontational" are need to examine their own reactions.
She ignored you and kept on behaving like that because she could see that your DH didn't have your back AT ALL and she enjoyed undermining both you and your DD and has probably left your DH with the impression that your household is not strict enough or that you personally cannot manage your own children. .... just as you are about to have number two. And her comment on that was completely crap too.
DD would be very aware that her dad sat there like a tailor's dummy saying nothing while all this was going on and will be left with the impression that she's a bad child - because of this stupid overbearing houseguest.
I think one of the reasons he just sat there and let you take "the blame" is the idea that he needed his friend to think that he was blameless and the "problems" can all be laid at your door. The way the sarky remarks were directed at you, not him, bears this out. Her ignoring your comments asking her to stop also bears this out.
Her behaviour was actually very divisive - you've already had an argument about it. He's already said you are in the wrong. She's had a lot of fun this weekend putting you and DD in your place, hasn't she - the big Knowall? It's as though she and DH were the two adults in the room. Patronising!
I'd be very cross about this and not just with her.
You need a very frank talk with DH for allowing this and continuing to side with this disrespectful guest.