[X] Plan - Seeing Is Believing
-[X] Call in help:
--[X] Saeki Nobuko.
---[X] Your own mother apparently isn't willing to unconditionally trust her own daughter (which is a bit sad). But there IS one person you know Midori seemingly holds an irrational level of faith in - that old fortune teller, Saeki Nobuko, who writes a column for the magazine your mother is the editor of. Given they worked together, your mother almost certainly has Nobuko's phone number.
---[X] Saeki Nobuko may sound like a hack on TV, but her powers are very real. Way back from the very beginning, before you ever joined the Guardians, hearing her words was what led you to give birth to Ran, Miki and Su. Later on, when Ikuto disappeared, it was Saeki's powers of foresight which allowed the Guardians to find him again.
---[X] Ask your mother to call Saeki Nobuko and request a reading on what she foresees if police were to be called the Scavengers' property.
---[X] Then ask what she foresees if Midori Hinamori were to go to the property.
---[X] And then ask what she foresees when Amu goes there.
--[X] Midori Hinamori.
---[X] Seeing is believing. If your mother insists in having a reliable adult accompanying Amu, she surely wouldn't object to it being herself. Your mother can draw her own conclusions when she gets there, rather than relying on anything Amu has to say.
---[X] You made a promise not to ask anybody for help or disclose the Scavengers' circumstances without first running it by them. So if your mother is that eager to help, even without your asking - she can go and ask them for the details herself and run herself by them. If the Scavengers want to lie to her face and convince her everything is fine... they are welcome to try.
---[X] When Kana was there at your birthday, there were few adults present. Your mother was one of the few - that freshly-baked cake didn't bake itself, after all. Kana will recognize her, perhaps Naomi too, if she was able to glimpse her before leaving. Whatever may be waiting there, your mother should be safe from the Scavengers at least.
--[X] Miki.
---[X] In the case there's someone at the house who aren't the Scavengers, Miki can invisibly scout the property and help to protect everyone in the event that it should be needed.
---[X] Though, obviously, not by using herself as a bulletproof vest.