Is there something like a USB female-to-female that inserts power "from the side" into the circuit?
Yes, it's called a USB hub. 😊
USB hubs aren't just multi-way splitters; they provide USB bus power to downstream ports. "Self-powered" USB hubs (the ones that come with their own power supplies) usually provide USB bus power for "high power" 2.5W (0.5A @ 5V) devices on all downstream ports. Note that 2.5W isn't enough power to charge even an iPhone, much less an iPad. The USB chargers Apple includes with iPhones support 5W (1A @ 5V) charging, and the iPad chargers support 10W (2A @ 5V) or 12W (2.4A @ 5V) charging.
Even "bus-powered" USB hubs are expected to provide power to "low power" USB devices on all downstream ports. But low-power devices are only 0.5W (0.1A @ 5V). I would guess than any bus-powered audio pre-amp would be a high-power device.
How can I power these devices using the setup described above?
The Apple "Lightning to USB 3 Camera Adapter" you mentioned — the one that actually has a "3" in its name — has an extra female lightning port so you can plug in your iPad charger into that adapter, so you can keep the iPad charging while using the adapter.
Note that traditional USB does not support sending power into a USB host port, so simply hooking the USB Type-A connector of this adapter into a self-powered USB hub via an A-to-B (host-to-device) cable will not cause the iPad to receive power. Besides, even USB 3.0's notion of "high power" wouldn't be able to charge an iPad. The only way to charge the iPad with this adapter attached is to connect the the adapter's female lightning port to a 10W or 12W USB charger. Any lesser power supply may be able to keep the iPad from discharging as fast, but to charge it up while in use, you probably need the 10W or 12W charger.
If your pre-amp is USB bus-powered, you'll need to put a self-powered USB hub in between the Lighting-to-USB-3 adapter and the pre-amp.