I guess I was lucky in some ways. My mom was very vocally supportive when I did my cleanse. I kept thinking it was reverse psychology. I remember her asking me everyday how do you feel? Arent you exhausted? Maybe subconsciously suggesting to me that this is going to harm me. ( Maybe thats me trying to read too much into it too!) Because if you do hear about this cleanse without reading any info on it it does seem far out and on the path to an eating disorder. Until you learn more about it it may seem that way.
My advice for you is to prove to your mom that you are not dehydrating yourself by drinking lots of water (in front of her) and consuming the calories of maple syrup by drinking 6-12 glasses of lemonade/ limeade. And maybe even saying to her that you will be looking fwd to ending the fast to eat a good healthy meal. So it reassures her that you aren't going to be on this for an infinite amt of time.