Has anyone created a Mac mini doc with a battery?

It does exist. It’s called an EcoFlow or Jackery battery unit. It will be big and heavy, but that’s what’s needed to power a 120 volt mini.

The problem with using them is that it’s pretty inefficient to provide 120 volts for the mini’s power supply, only to down convert the voltages to what the logic board and components use. You’ll need way more mAh than you’d need to just power a MacBook.

If you want to travel occasionally what benefit would this proposed setup have, over a MacBook Pro? Even if you add in a dock/hub to get more ports (e.g. the mini has wired ethernet), it's still less faffing around, likely less cost, and gives you a bigger screen than the iPad, without the issues inherent to using an iPad as a computer screen.

It isn't 2002. Laptops with features comparable to desktops do not require a three point lifting harness and a recurring appointment with a chiropractor.

For reference, I've used a desktop as my primary workstation since late 2018. For the ~decade before that I used a laptop as my primary workstation.

What about leaving the mini at home and remote desktop from the ipad? Probably still inferior to a macbook, but sounds better to me than a battery powered mini.

Use an EcoFlow

At that point I'd just get a MacBook.