In my mind, they communicated through texts because she was likely on the bus headed to the tea shop initially, and didn't want to broadcast the issue for everyone to hear, and she hasn't gone into detail due to being at the pub. She will divulge further information when they're alone, because she definitely trusts Alex but not anyone else around her. I don't think she has a car at the moment; we can say it's in the shop or something otherwise she'd have just gone to the ranch by herself. She likely doesn't need one. The law firm would have several 'loaner' vehicles, and drivers that Adrian sends for her if she needs to go somewhere. If she needed to teach at the school, one of the other teachers would pick her up until whatever is wrong with it gets fixed.

I also think they should get the hotel room for the evening, and let Adrian find them in the morning. They'd have a joint back account and when she doesn't come home that night, he notices the charge for the hotel (Cora will insist she pay, since Alex drove all the way to her) and goes to find her - unaware that Alex is also there. It'll also give us a little more time to settle into their characters, and have a moment of 'calm before the storm' so to speak.

Edit;
If I went too far without your approval, let me know. It isn't far, really, but I just headed with the agreement of the hotel room and the girls leaving the pub to Alex's Jeep.