I think you need to not have an argument but discuss with your husband how things are changing, your daughter is growing up, she is an adult now and that what she does is her business.
Where does he see this going if it turns into a battle of wills? The ultimate response to "under my roof" is her deciding to move out, is that what he really wants to happen?
Has he thought about when she's "allowed" to go private? When she's 21, 25, 30?
What behaviour is he trying to encourage by setting these controls, is it working?
What is he doing to readjust to their new relationship as adults? These are all things he actually needs to think about, rather than getting in a row.
The "not our house" thing also needs addressing, but at a different time. How does he think he would have managed providing child care when your kids were young if you had not been at home? You sacrificed things to stay at home, a blip in your career at the very least which would have had a negative effect on your future/current earnings if he wants to take it to pounds and pence.