C Doubly Linked List
As mentioned in the comments this code is not long winded at all.  It is very clean in general.  Too clean in fact as you will see below.


You cannot create an empty linked list with your init_list.  However, in other parts of your code you assume list may be empty.  It is useful to be able to create an empty linked list since you may not know what you want your first node to be in advance.  I'd suggest changing init_list.
I personally like symmetry in linked list code.  You can always create the dual of one function by swapping all prevs with nexts and all heads with tails.  I don't think your push_back code should call push_front.  You can handle the else condition just like you did in push_front except by swapping variable names.
insert_after is incomplete.  Remember this is a doubly linked list.  Also the function doesn't handle the case when you insert after the current list-&gt;last.  You need to add the linked list to the function arguments.
remove_node does not handle all cases.  What if node was the head of the list?  What if it was the tail of the list?  What if it was both the head and the tail?  You don't actually have to write three different cases to handle this but you can.
As simply a style choice I would rename previous to prev
I am ignoring that you never check for your pointers being NULL


Edit:

This code actually can produce an empty list by passing NULL in as an argument to init_list