Display children's children menu automaticly after adding children page

Hello,

My customer wants me to do this thing. Let me explain.

I have main menu. On the one page of this menu, there is another menu – child menu. The problem is, I when I click on any page of this child menu, that menu dissapears. I have one solution how to call for it, with page_id but my customer want to add child pages by himself, so it should work like if he creates page in child menu, child menu should automaticly show on that page. How to make this happen ? I tried some tutorials, but any single one wasnt what I exactly need. Can someone help me with this ? Thank you

Menu:

mainmenuitem1
mainmenuitem2 (if someone click here, child menu will be displayed)
-childmenuitem1 (if someone click here, this menu will be still displayed, wont dissapear – same on childmenuitem 2 and 3.)
-childmenuitem2
-childmenuitem3
mainmenuitem3
mainmenuitem4

I hope you undestand me. Thanks