My husband is a FF (not in OP, though), and the answer you're getting doesn't surprise me.
Fire stations are generally not set up for that sort of thing - most have a bunk room (sometimes split into individual cubbies), bathroom(s), kitchen, and "day room" (basically their TV room), and maybe some offices for the captains or other officers stationed there. Kitchens and day rooms are often pretty bare-bones, and in DH's department, are generally furnished in hand-me-downs from the guys' homes (think "bachelor pad chic"). There really isn't a space for a "gathering" of any sort, and if there's room, well, it's not exactly the sort of setting you'd probably want for a children's party.
The only other spaces in most stations are the garage/"bay" where the trucks are and maybe a gear room -- places where it wouldn't be safe to have a group of children. A few places might have a "training room" that would be set up with tables & chairs, but that would be rare - probably less than 10% - and due to training equipment that may be stored there, those sorts of places may still not be suitable for small children.
So, my suggestion would be to either do the tour and then presents/cake at another location before or after the tour, or just skip the fire theme for this year and take some more time to inquire around about other stations that might have a suitable party space. I'm sorry - I know that's not the answer you were looking for.