How do I water potted outside plants while on 3 week vacation?

If you have a lawn sprinkler system you could make sure the plants are situated where the spray will water them. Otherwise, I would seek the help of a neighbor or a friend who lives nearby.

hire a neighbor kid

3 weeks is a long time...........you could try putting them in a child's plastic swimming pool filled with water, and then ask a neighbor to replace the water as needed.

Set the pots in two rows. Place a hose with a fan-type sprinkler between the rows. Lower the water flow to desired level. Put hose on a timer.

I have poked a 2 liter bottle with bottom cut off upside down in pots like a funnel and fill with water. 3 weeks is a bit longer so I agree, maybe someone else could just check and fill the bottles again.

I used gallon milk jugs, fill with water, take old rags (old tee shirts, old towels, etc) tear into strips about 3-4 inches wide by approx. 2 feet long. Place one end of the strip in the gallon jug, make sure it puddles slightly in the bottom, take the other end and lay on top the dirt, that also needs to puddle. It worked for me, don't know how long it will last but after a week it still had about half the water left and I live in the south with hot and humid days.

I fill wine bottles with water and then tilt them upside down so the open end is in the soil. I use it like a "water globe"