You really need to be firm with her and say that this time you would just like to share the experience with your DH. Sorry to say it but if you don't lay down some ground rules for her now, she is only likely to get worse as the pregnancy progresses and when baby arrives.
The hospital that does our scans only allows one other person in the room. That is a good excuse to use. And I agree wholeheartedly with other posters saying just do not give her the appointment info in future.
Tell her your hospital allows one other person only
Tell her that it has to be just you and dh - without wanting to be a downer, how would you feel If an issue was found during the scan? You'd be very upset - this isn't a nice jolly baby viewing expedition for your mum, it's a medical screening procedure.
If she wants a nice jolly baby viewing trip, then arrange one of those private baby view scans after you've had your screening results.
Also, you need to get boundaries down now. If she's trying to crash your scans I think you can expect more shenanigans like this - a bit of it ting your foot down now will save you from one of those "mother wants to be in the delivery room " threads in a few months time.
Tell her no. And repeat until it sinks in. Then in future don't tell her anything about appointments etc. Have you told her your EDD yet? If not completely fudge it otherwise she will be camped outside your house waiting for you to leave for the hospital in 6 months time.
Also when you do go into labour don't let anyone know you are at the hospital until all is well or even until you are home again if you don't want visitors on the ward. Otherwise it seems like she will either be bugging the staff ringing up every few minutes for up dates or turning up next to you holding a leg as you bare down.
Just say no.. Upset or not she'll get over it! My mil turned up to our gender scan too which i wasnt happy about! I was already up on the bed when she knocked on the door! The lady doing the scan asked me if i was ok with her coming in infront of her so i couldnt say no! So she found out the gender with us! In future i will not be telling anyone when our scans are!
you have said you don't want her there - she has said she is coming anyway. Does that sound like she cares about your feelings? So no need to pussyfoot around hers. Nip this in the bud and make it clear that it's YOUR baby and whatever you say, goes. Otherwise, next thing you know she will set up a nursery at her place, insist on being at the birth and have baby overnight the first week..