Too complicated.
Begin at the beginning - see if the wine-barrel holds water, then deal with it. Note that a dry barrel may leak, but stop leaking once it's wet & swells. There are ways to do this that I don't remember... Youtube will know.
If leaks, a liner's an option & likely safest & works if the timber's still wet, though also ugy & clumsy & not cheap. Have a look for sealant paints for potable water tanks, often in 2-part either in epoxy or a polyurethane. You won't need much, maybe start by stuffing and/or calking any obvious leaks or holes - either mark where water comes or find with flashlight at night. Having said that, you might be able to get away with a tube or two of brown 5200 and/or some putty-epoxy, for example. Maybe start this conversation at the marine-supply shop (West Marine or BassPro?) as you're essentially creating an inside-out boat
Note: not "normal" fibreglass resin, as the Polyester is hydroscopic. Having said that, it'll probably last the season, just remember to re-do in the over-winter.
Re stocking: if you're mum's liking lilies & lotus then you'll loose some water-volume to soil/mud, which is fine as you won't have space for monsters anyways. A bubbler's a nice idea, or a small water circ-pump, but don't bother with filtration as you'll be picking up a lot of your soil. Rework the whole thing at end-of-season if you feel to.
Stock with from-top pretty stuff that won't get O2 starved on hot days: guppies, swordtail, beta, gouramy, paradise - you'll be less limited than you expect. Even groovinesses like arowana, af/asian knives, af.butterfly, chana, gar & some cats/pleco will have some capacity for atmospheric air, though each will likely be "out" for its own reasons. So it goes. Ramshorn/mystery snails & a FW clam/mussel might help to keep everything digested & the water crystal.
Have fun!
