I can't specifically answer for dimension tables or SSAS. My answer is just in regards to how identity columns work in the parent and child tables. The order of the columns in a table doesn't matter.
Here's an example, I didn't take the time to add PK or FK constraints:
create table Parent (ParentID int identity(1, 1), name varchar(50));
insert into Parent (name) values ('Tara'), ('Dean'), ('Samuel');
create table Child (ChildID int identity(1, 1), column2 int, column4 varchar(10), column3 int, ParentID int);
insert into Child (column2, column4, column3, ParentID) values (24, 'test1', 5, 1), ( 999, 'test2', 0, 3), (8765, 'test3', 1999, 3), (77777, 'test4', 22, 3);
select * from Parent;
select * from Child;
select * from Parent join Child on Parent.ParentID = Child.ParentID;
drop table Parent, Child
ParentID is how these two tables are linked. Doesn't matter how many rows are in the Child table, ParentID still links up to a row in the Parent table via the ParentID column in both tables.