Sounds as though you don't need a lot of pressure (just enough to get up 5 feet or so) but are you concerned about flow rate? If you're not in a hurry, you can get a 280gph submersible 12 volt pump from
https://www.goldmine-elec-products.com/prodinfo.asp?number=G20108
plus another $5 for 15 additional feet of waterproof cable. Plus shipping.
The pump's output is 1/2" so you'd need an adapter to connect to your garden hose (short piece of hose that will fit the output and proper hose fitting on the other end.
You said "southwest corner" so you might have good sun there. If so, you could run that 12 volt pump from a battery that's kept charged by the sun. Not cheap but cheaper than having an AC outlet placed nearby by an electrician.
30 watt solar panel $60 (Aleko panel, Walmart) adequate to recharge in 3+ hours of sun - if you have less sun look on Ebay for a 100 watt panel ($85 delivered)
20 amp solar charge controller $20 (#300186, banggood.com or similar - EPEver makes good units but at twice the price)
35AH AGM battery ($70, batteryclerk.com, Harbor Freight, others)
On/Off switch for the pump (Advance Auto, AutoZone, Walmart)
some 16 gauge wire (red and black, (Advance Auto, AutoZone, Walmart)
inline 10 amp fuses $6 each - one for solar panel, one for pump (auto parts)
miscellaneous butt connectors for wiring, etc.
You figure out how to mount the solar panel facing south. On the roof is ideal but at least high enough to be out of easy damage reach (careful with the shovel over your ahoulder ;-)
The pump should either be suspended 6 inches or so above the bottom of the barrel to avoid picking up trash OR you could make a floating pump with some waterproof foam (think: floating boat dock) and the pump would always be drawing from the top few inches of the water, regardless of level (this assumes a barrel with a removable lid).
With an open hose, that pump can empty the barrel in about 12 minutes so you might want to lay out soaker or sprinkler hoses instead of hand watering and just run the pump for 2 minutes every hour or until the soil is "wet enough".
I sized the battery for several consecutive days of use without sun and to handle the startup load of the pump.
The solar powered lighting in the equipment shed out back is my design and is in it's 17th month of reliable service.