YANBU, you're being human. You're not a shitbag, or a let down, you sound actually rather nice.
Its healthy to feel a bit shit sometimes, shows you have a conscience, but you also need to not let it run away with you.
Regarding your mate, explain to her. She may be disappointed but would she seriously want you to get into debt just for a jolly to vegas? As an alternative, maybe you could do something closer to home? A weekend away perhaps? Or invite her over, get your OH to dress as a croupier, and have an at home casino night to make up. Could be a laugh.
As far as your 3yo is concerned, I do think that sometimes, our kids need to be aware we're human too, and we all have off days. Your DS is going to have to learn that he's got a sister now and mummy's time (not love) is split, so he needs to behave! Regardless, you are human. There's 4 yrs between my boys and I remember that it wasn't easy when my youngest was nb, its a whole new dynamic that everyone's got to get used to so don't kick yourself if you have the odd off day.
Chin up... YANBU. Oh and its also OKAY to have a bloody good moan about it at times as well.