I want to make this cake for my mother's wedding this summer, but I've done 3 test cakes and had the same problem each time: the cakes shrink away...

If you are baking the layers in a large diameter pan, they are probably not cooking through in the middle {I had the exact same problem when I made a wedding cake in a ten inch pan, it was too dense}. You want to invest in a heating core. Ateco and Wilton both make them. You stick it in the middle before putting it in the oven and it will cook the center.

If you are weighing all your ingredients, you might be adding too much baking powder. Since it is such a light powder and the amount you want is so small, the baking scale would not be able to accurately measure such a small amount. Unless it was one that measures out to 0.1 (tenth) decimal place (and that can be one expensive scale). Too much leavening and the cake rises so much that it could not hold it's own weight and thus collapsed in the middle. Here's a full explanation, http://whatsarahbakes.com/2015/11/18/why-did-my-cake-sink/

Good luck!

The creaming method is very tricky because there are so many factors to consider. Is my butter too soft? Am I over creaming? Am I under creaming? Am I overmixing the dry ingredients? So on and so on. When I cream butter and sugar, I generally start with the same procedure: COOL but pliable butter. "Room temperature" leads to a lot of interpretation and inconsistency, so I just make sure my butter is "moldable" instead of soft. Get the butter in the mixer first to loosen it up and slowly add the sugar (I also add salt for a bit of extra abrasion). Beat that until pale yellow and fluffy. You should be able to see the air captured in the butter (there are resources online to help with that visual). If you're sitting there watching the clock, and not relying on your senses, there's no telling what you're going to end up with. I usually cream for around 4 minutes like the recipe says, but if I don't watch it, I might end up with breakage. With a white cake, I only use my mixer to do the heavy duty stuff: the creaming. Everything else, I do by hand. So I dump my mixture into a bowl. Clean it and whip my egg whites. While they're whipping, I sift my dry ingredients over the butter/sugar and fold it in. I don't fold it in all the way, just mostly. Then when the egg whites are firm, I fold them in just to incorporate...this will incorporate the rest of the dry ingredients. I say "firm" with the egg whites, because you don't really want fully stiff. The egg whites are going to expand in the oven, and you need a bit of room for them to do that. Fully stiff egg whites are going to stretch less than firm ones. Firm is just past medium, but just before stiff. It seems like a weird visual, but its actually very simple. Just as the whisk starts to make trails in the meringue, you lift it out to see the peak. It should stand, but just curl at the end. Also, when beating eggs to stiff, it's easy to over beat....and then game over.

Something else I started doing a few years ago was doing the reverse creaming method for white cakes. Cook's Illustrated and Rose Levy Beranbaum have written about it. It's easier to do, leaves less to interpretation and works every time for me. You could easily adapt this recipe to that method (leaving out the cream of tartar). I ALSO never bake a white cake over 325F. But that's my preference.

And lastly, what others have mentioned, most cakes (especially leaner cakes), shrink away from the sides a bit. If you're afraid of under baking, you may be over baking...that will cause more shrinkage and collapsing because the proteins are constricting from over coagulation. So, bake until you have a little bit of crumb on the skewer or, if you have a probe thermometer, to 200F....that's the temperature at which most baked goods are done.

Good luck! I think you're on the right track. White cakes are perfect for wedding cakes because they're light but sturdy! Let us know!

I wonder if you could be under- or over-creaming the butter/sugar, or getting it too warm. Any of these problems can cause overly dense baked goods. There's a really great guide (with pictures and a video) for creaming butter and sugar here (http://www.seriouseats.com/recipes/2015/12/soft-and-chewy-sugar-cookie-recipe.html) from Stella Parks, Serious Eat's pastry expert. It's in the context of making sugar cookies, but the same rules apply for any recipe that involves creamed butter and sugar.

Are you at high altitude? I had a similar issue with cakes (I'm at 4500'), until I found something that said to use let fat & less sugar. So now I use about 1T less butter, and a couple tablespoons less sugar, and my cakes have been much better...

Maybe others will be able to suggest solutions to your technical problems.
My thoughts are more how to get a cake you and/or the guests of honor like for the wedding. So my ideas, like HLA's, are also work-arounds.
Do you have a reliable cake you've made before that you could substitute for the one that is giving you these shrinking sides and dropped middles? And then apply to that cake the raspberry & lemon filling/buttercreams.
Or, yes, turn to Rose Levy Beranbaum Cake Bible. I've made half or more of the cakes in that book and the recipes are reliable, delicious, beautiful. Many are like a little black dress, which you can serve simply or dressed to the nines.
Last, in the back of this cookbook there's a terrific section on wedding cakes, with professional tips and sources for ingredients and tools. No, I've not made a wedding cake from the book.
Good luck with the cake and congratulations to all!

This is not exactly an answer, but some ideas & a work-around option. It's definitely normal for a cake to shrink from the edges after baking -- and with large diameter cake pans before you pull it from the oven. It's also normal for them to lose some height after they come out of the oven. It sounds like the biggest issue is the sinking, which in my experience happens when the cake is not fully cooked through. In addition to the toothpick test do you do the spring back test? The other common culprit is not enough structure to the cake. So it may be that your measuring technique for the flour is giving you a little less flour than what Erin gets when she makes hers. Try measuring by weight rather than volume and see it that works better. I imagine Erin would be able to give you a weight measure; depending on method of measure weight of AP flour can vary from 4.25 ounces to 5 ounces per cup. AP flour has more gluten & therefore can build more structure than cake flour so it may be a better bet than cake flour. You could also try decreasing baking powder slightly -- it's a balance between the leavening and the cake getting gelatinized, so maybe a 1/4 teaspoon reduction will help. Per the Cake Bible it's best to alter the baking powder depending on the size and shape of the pan. I assume your pan is 8" round, but if it's square that could be the issue - a square cake needs less baking powder (82% of what an 8" round needs).
You could try baking them with cake strips to help them stay level during baking. https://www.youtube.com/watch?v=aAtM2Gaf1Xg Whether this will prevent the sinking in the middle I can't say, but it would be worth a try.
If you can't get the cake recipe to work for you, then you could always use a different cake with the same filling and frosting. Maybe rather than making numerous attempts at this recipe you will be happier with a different, tried-and-true recipe. I've had great success with Rose Levy Beranbaum's cakes from the Cake Bible -- you could make her white butter cake and add lemon zest, or if you go with yellow butter or the golden almond cake. The other beauty w/ her book is the section dedicated to wedding cakes that helps you scale for the size pan you need. The book is definitely worth a gander if you are making a tiered cake.