1)
If you are talking about your wife:
My wife went to work and took the key with her. Then, when She got home, She found out I've been locked out.
If you are talking about your son or your brother:
My brother(son) went to work and took the key with him. Then, when He got home, He found out I've been locked out.
Well, I would say someting like:
"Well, you might pay more attention next time, It's really annoying being locked out of my own home"
If it is really happening with you, you should just get a copy of the key hahaha
2)
You could answer with something like below:
"Sure, we can set this up!"
I guess this would be right. Since i'm not a native, someone could correct me if I directed you on the wrong way.
Thanks