Agree with diddl, surely they are both to blame. Did your mum not notice your son kept on walking with your dad rather than staying with her?
Unless the plan for her to go to the park with both children changed, say if your dad said to your mum oh it's ok he can carry on walking with me, you go to the park with youngest. Then perhaps she assumed your dad would then accompany your son back to the park after walking the dog with him. She may have assumed he had the sense to walk your son back, I think my mum would assume my dad had that common sense if this happened to them. If they verbally changed the plan then I'd say she is less to blame.
But if no change of plan was mentioned between them then sorry but I would blame your mum and dad equally. In this case why wasn't she watching her gc who managed to wander off after your dad?
Your dad should never have sent a young child off back to find your mum by himself. Then again my parents are getting older, in their 70's now and I've noticed they have sometimes forgotten what it's like to have young children. They have done some silly things like leaving sharp things out, I've mentioned it and they said they just didn't think. Telling a 4 year old to walk back by himself to find his nan is a bridge too far though, I'm assuming you mean your dad didn't stay to watch his gc reach his nan safely if she was within sight, and that it was a fair distance for your son to get lost for 20 mins?
If you have a normally happy relationship with your mum then I'd assume she is crying and can't talk because she's in shock and so upset. Has she actually said she blames you? The only reason I'd think my mum is blaming me is if I have a narcissist for a mum who regularly employs these kind of tactics and diverting blame away from herself with drama.
If your mum doesn't do that kind of thing normally and you have a good relationship, I'd say she is actually in shock, angry with herself and your dad and can't function right now. Like others have said, if that's the case then I'd take her up a cup or tea and give her a hug, then find out all the facts on what happened. She is probably feeling ashamed and that you are (rightly) angry with her. If I had lost a child, anyone's child, even for a minute, I'd probably feel physically sick, and after 20 minutes I'd be feeling very physically unwell from the stress in all sorts of ways.