Jadey I'm so sorry this is causing you so much anguish. It must be a very upsetting time for all of you.
I've been thinking about it all afternoon and have read what other people say and agree with all that they've said - particularly about a "listening ear", explaining situations properly and remaining calm, positive and reassuring, etc.
However, one or two things did occur to me, though I don't know if they are relevant/helpful or not.
Would it be helpful to establish a set routine whereby on a particular day and at a particular time each week (or more if possible and if mum and dad think it appropriate) daddy rings your grandson, so it is not just when he is anxious and upset that he speaks to his daddy on the phone? Children seem to find set routines reassuring and comforting.
You say this behaviour has only started "recently". Has anything happened lately that may have unsettled him - if he goes to nursery school, has there been any change in staff or children attending? Has there been any other change of circumstances that might have unsettled him? Sometimes small and seemingly insignificant things can worry young children - when I was about 5, I wouldn't go to school because I had made a small mistake in my arithmetic book and was worried the teacher would be annoyed.
As others have mentioned, children feel anxious when their parents argue and, even if your grandson doesn't hear arguments, is there an underlying feeling of anger and resentment between the parents? This is natural if there has been an acrimonious break up but I wondered if it would help if the parents sought counselling - either separately or together - to assist them in gaining insight into what triggers arguments and how to deal with disagreements in a less confrontational way. (I hope you don't feel I'm overstepping the mark here, but several years ago I found it very calming to talk to a neutral, non-judgmental counsellor who helped just by listening).
Is it possible that your grandson is worried that his daddy is alone or lonely? I'm not suggesting that this is the case, but, now that he's older, your grandson may be imagining this and possibly feeling guilty. Maybe he needs reassurance that daddy is safe and happy. Also, do your son and his ex respond to your grandson's distress by becoming panicky and distressed themselves. It's probably better to remain firm, calm and reassuring, and try to distract him with a task - like "let's draw a picture for daddy and send it in the post to him" - so that he feels connected even when you son isn't physically present.
Most children go through periods of "clinginess" and crying. When our granddaughter stays with us, she cries terribly when her parents leave (and vice versa) but after a very short while, and with a little distraction, she's happy again.
You are obviously a very caring grandma and mum, and, with your love and support, I'm sure this difficult phase will pass.