it's difficult when your small children grow up to be semi-adults. You need to constantly reasses the relationship, and how the family dynamic works.
first of all: your DH shouldn't have shouted at you, but at least he initially stood up for you
Your daughter was being a pain in the neck, and definitely shouldn't have shouted at you and stropped off. I hope there is no financial contribution to me made for the AA call out that you will cover?
Now you have to decide how this relationship, with you all under the same roof, is going to work. If, as pp said, this bf is always there and constantly helping himself: that needs to change. Work out between you and DH what you can accept here. The least number of overnights/hours that is acceptable to one of you "wins"
Laundry? She is having a huge laugh. She gets a laundry basket and you and DH get a laundry basket (keep it in your room if you must, to stop her dumping her things in it. She takes care of hers. You and DH take care of yours. (depends how you want to do it. I see on MN that many people seem to only do their own. DH and i share laundry duties and do each other's. Decide what works for you)
Does she earn? pay rent? how much extra is she costing you in nerves, hours and actual readies? Work out what is acceptable, and how much she should contribute (either in doing things around the house or money).
Agree that if it gets to shouting, any shouting by anyone, the discussion needs to stop there and then and will only be talked about when you are all calm.