but with it designed for the opposite flow of water.
I have a rain barrel that is usually at least half full and it provides enough pressure to use but it's not enough to water my garden efficiently.
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I wouldn't risk connecting the rain barrel to your house's plumbing because you don't want to risk getting non-potable water into your pipes. This sort of arrangement might even be illegal where you live.
What if, instead, you just use a garden hose to add more water to the barrel as needed? Then you don't need to worry about running out. Or, use a quick connect fitting to make it really easy to disconnect your watering hose from barrel and connect it to another source.