First of all: You are doing a great work by serving those who are in needs.
Secondly, it would be helpful if you could write something about your device: like electrical parameters, working principles, etc. I guess you are providing solar powered inverter set-up with inbuilt battery in it? And when there's no sun or any power supply, you want to be able to charge your inverter's inbuilt battery with a heavy capacity external battery??? If this is the plan, then ofcourse it is possible.
One advice: Although it is expensive, but try to consider using ferrite core transformers as you want your device to be most power efficient.
Can we build an external battery that hooks into the back to the DC charging port that solar/AC charger use to charge the internal battery.
Yes. But if you can provide external batteries separately with your device, why to charge the internal one with it and waste around 30% of charge in charging process, while you can shift the back-up from internal source to external one? Is there a specific reason? Or maybe I am not clear what your current technology is.
Is the circuitry complicated?
Not that much. But to charge a 12v battery, you need at least 16v. So if you use an external 12v battery, you need to somehow increase its voltage by designing another inverter-transformer-rectifier circuit (matching output of the AC charger you have), with a very considerable size and weight of the transformer because charging current will be over 10A (I guess). This might make it a little heavy and bulky with unsatisfactory power factor. Plus it will dissipate heat, which prompts a cooling ventilation. Maybe it wouldn't be much consumer friendly. But it all depends on what you already have in hand, what you can invest and what you can achieve.
Can we make a robust & attractive housing?
Yes. But embrace the fact that using an external battery to charge the internal one demands it to be another inverter device, not just an add-on tool. So you have to decide if the housing will be only for the circuitry with bare battery, or the battery-circuit combined.
Li-ion batteries have much higher density, but it is expensive and it's charging is complicated. Plus they tend to explode when they heat up or due to manufacturing defect. SLA batteries are little bulky but cheap and readily available. They also don't need maintenance. And it is better to provide lead-acid batteries
only if your end consumer knows what acids can do.