This is inappropriate. Not super common but I have seen it happen before. Actually, I guess I shouldn't say it's not super common- it varies by the floor. Floors where patients are inpatient for longer tend to have more of this. I know it was something that happened with relative frequency on the Stem Cell transplant unit of my old hospital.
The ONLY time I would ever call the hospital to check on a patient would be if something happened on my shift (i.e. a rushed a baby to the OR at change of shift) or I was a primary nurse for an end of life patient and I wanted a general idea of what had been happening before I had to come in and take care of him. And in this situations, I would always call the nurse caring for the patient or the charge nurse to inquire about the patient. Would NEVER give a parent my cell phone
number and have them text me with questions when they have a nurse caring for their child 24/7, that's who they should be asking.
It also undermines the nurse caring for the patient when nurses do this... if you're trying to take care of little Sarah in a crisis but Kelly is her primary and has given mom her cell phone number, how would you feel if in the midst of assessing Sarah and trying to get her to wherever she needs to go (CT, the OR, ICU, etc), the mom says "I think we should call Kelly." Um, no. And, what kind of nurse wants people calling them about work on their day off? No, thank you.