I tend to disagree with most of the above posts. I can completely understand your anxiety about leaving your son especially since he is still so young. 13 months is still so little. I don't think it's unreasonable to ask your mum to go to the appointment with you and DS.
Is there a reason she feels she should stay at home with him? Does she understand how anxious that would make you?
I agree with others who said one step at a time. And I think a great first step is your mum coming to the scan and taking DS for a walk or something. You will have many more scans in your pregnancy and there will be plenty of opportunities to increase the amount of time she looks after him. I would also have a serious conversation with her about the way you feel. Good luck!