Setting Level 2 to "Hide from Menus" will hide its children too.
You could use the property levelClass:
[[Wayfinder? &startId=`0` &levelClass=`layer`]]
That assigns a class="layer1" to the item Level 2 and a class="layer2" to the items Level 3.1 and Level 3.2 (because the counting starts at the children of the top level).
If you then define this rule in your CSS, it should work:
li.layer1 { display: none; }