There are multiple levels to the OP's question.
1) The shop's policy is BS. There should be no "requirement" to take AOW immediately after OW, if they are doing their job properly in the first place. It is certainly possible to pass new OW students with all the skills they need to safely dive within their training constraints (60' max, similar temps/conditions to those they were trained in, etc.).
2) That said, point #1 is wasted on the OP, who has already received training from a shop that teaches rushed classes which probably do not prepare her very well for diving without instructor/DM supervision.
So what are the choices, in her situation? Well, certainly you can kowtow to the shop's insistence, spend the money, and take AOW. Hopefully the extra dives will give her the extra skills and confidence her OW course lacked. However, I suspect that's not the best option. As others have noted, there is actually at least
some value to the actual AOW course dives, and frankly, a new diver who is struggling with basics left over from OW is not going to benefit as much as if she had the basics a little more dialed in. However, as someone also noted above, it's also true that if you wait too long, there's very little benefit to be gained from AOW, since most things can be picked up relatively easily without the class.
So what's the other option? There are two options that are quite good, to my way of thinking: IF the OP is actually fairly confident in her skills, she could take the AOW class and benefit from it. If, however, she thinks some easy dives spent dialing in skills would be a good idea before attending class (I agree in most cases, and I'm guessing she does, too, else why post this thread?) then absolutely she should get some dives in first. Some ideas thoughts for that: (a) Make them nice easy dives in conditions similar to those she's familiar with, from her training dives. Or, (2)
hire a local DM to take her on some easy dives. Or, (c) find an experienced buddy to dive with just for a few dives, to keep an eye on you while you're still getting comfortable. Not a buddy you just took OW with, but an actually experienced local diver.
There's no need to spend a lot of money to take a full-blown AOW course just to get some supervised dives. In many (possibly most?) locations you can hire a DM (or even an instructor) for a couple of supervised dives... no need to clutter up those dives with course information before you're ready to focus on the course information.
After a few dives, say 6 or so (bringing your total # of logged dives up to around 10-15 or so), go ahead and take AOW, from a more confident standpoint, and then you'll be ready to absorb the information given in AOW more readily. I'd much rather see an AOW-graduated diver with 15-20 dives than one with 9.
This is the approach I'm taking with my wife. After her OW course's 4 dives, I plan to take her on 6-10 easy dives before she takes AOW. Since I'm a divemaster, it's a little different for me, but not much... she simply doesn't need to hire me to accompany her.
Whatever you choose, good luck, and dive safe!