As Bend stated, your scenario won't satisfy the defence of necessity. After all, if it truly was an emergency, all you had to do was pull over and call 911 so that they could go pick up your mom. We have emergency vehicles for that purpose with specially trained staff. Your involvement would not be considered essential to justify breaking the law.
By the way, if you held your cellphone when your wife called you, that too could have yielded a ticket for drive with hand held device. After all, it would not meet the definition of an emergency situation since you wouldn't have known about your mom's situation if you didn't pick up the call in the first hand. For all you know, your wife could have been calling to ask you to pick up bread. The emergency exemption on the cellphone would only have applied if you were actually using it to call first responders (i.e. an emergency).