Consider following the guidelines of folks who actually created something similar to what you want. For the most part, when it comes to creating large props, builders will go with the tried and true stage set walls or flats. How complicated and sturdy you make them really depends on how long you're going to have this archway around before your wife decides you really need to build something new.
The image above is a prop made by the pair at Hollywood Haunters. It's created by putting together a mosaic of set flats. You can watch them throw it together in their video
Just about everyone does something similar. Even HauntedWyo's wonderful mausoleum is basically four stage flat walls joined together. If you're willing to search around, you can build them for very little, but it does take a bit of running around to find free foam, wood, and the like. Still, it's what we do. Our cheapest mausoleum facade cost us nothing, and our most expensive facade cost maybe thirty bucks because we have store bought parts to it.
Depending on what you want to do, you can build a simple facade that looks like what you want from the front, but looks like a prop when you walk past it. All of ours are that way because once the kids are headed up the stairs for candy, they really don't care what the backside looks like. You might wind up making a free standing prop that looks real on all sides. It's pretty much the same thing, just joining all those flats together in a way that works to give you what you want.
And true to Harry Potter in the real world, you're going to use foam to create almost everything. Making it hard coated costs a bundle, so most of us leave that to Universal Studios, but even that is something you can do given the right budget. Our budget says we fix the dings that happen along the way.
