This is working:
create table table1(id int primary key,uname varchar(10))
create table table2(id int primary key,id_2 int,uname varchar(10))
go
create trigger i_table1 on table1
for update
as
update table2
set uname=inserted.uname
from inserted where table2.id_2=inserted.id
go
insert table1 select 1,'test'
insert table2 select 1,1,'test'
go
update table1 set uname='test2' where id=1
select * from table1
select * from table2
Try to find error in your script.