I agree.
The situation was getting tense... you took your toddler and yourself away from it. That sounds very sensible to me. You and your DD had a break from some permanently bickering and fussing boring adults who should all know better.
It was all stirred by MIL who has been bickering all holiday and is het up - who refused to pass on your message to your DH.
As for the drunk eye rollling FIL, bursting into tears - its absolutely pathetic. No one died. No one was seriously injured. What is wrong with your DH.. I understand he's in the middle but he's really buying into their nonsense with the whole Grown man only cried four times in his life rubbish.
Eye rolling at a preg in 3rd trimester asking partner for help would really annoy the hell out of me too.
Toddlers do fall and often on furniture, especially in a strange house.. We had to put bubble wrap on the corners of our stupid coffee table for a while (which DH hated) but it saved both me and DS a lot of botheration.
FIL is a parent so he must have experienced this before... but I also hate GPs attempting drunk supervision of young children and I don't blame you at all for leaving such a fraught situation.
The fact that they all made such a HUGE DRAMA out of you taking your DD, who they were clearly getting annoyed with, out of a tense situation to a nearby park for a breather to everyone, speaks more about how difficult they all are.
The constant bickering and fussing must have been unbearable.
I absolutely guarantee that if you'd stayed... they would have kicked off even more - and particularly at you. As the outsider - you've been designated lower in the pecking order, which is fab for them as they have someone they can easily blame.
Be careful about over apologising and grovelling to DH (as he seems to expect) (as poster above said) it will make it appear you are more in the wrong than you really are. You've apologised. That's enough. They accept it or not. If they can't that's their problem... what more do they want from you?
You are about to give birth and DH needs to have your back not berating you about his Dad's emotional problems, but he's caught up in the family dynamic. And its really stressful having to watch a toddler around a difficult dog and drunk adults. Not the dogs fault but equal level of supervision is required. What is your DH doing?
When you are with a bunch of argumentative people who can't contain themselves and are all looking for someone to blame or an excuse to kick off and vent their "feelings" the only thing you can do is retire and say "Serenity Now!" on repeat.
Then keep your cool. Don't engage with nonsense. Make a decision to manage your DD. Ignore suggestions/comments/eye rolls. Take her into a different area without annoucing when it all gets to much. And then carve a bit of space, or this bunch are going to be a nightmare when baby arrives. I'd quietly make a plan now about visiting/how to manage dog near new baby/toddler when youre attention is divided and tell DH what you expect in this regard.
Have you got any support from your own family? If so lean on them.