Reddit mentions of Powermax PM4 35A 110V AC to 12V DC 35 Amp Power Converter with Built-in 4 Stage Smart Battery Charger

Don't worry too much about the input (120 volt) input - in terms of input vs output, watts are going to be close to the same for a battery charger. That means a 12 volt, 20 amp charger is going to put out about 300 watts (12 volts x 20 amps is 240 watts, but a lead-acid battery charger is going to put out close to 14.5 volts, which is technically 290 watts - I'm rounding). That means the input at 120 volts is going to be about 1/10 of that, because the voltage is 10 times larger. I say about, because there are always losses due to heat and efficiency, but most modern power supplies should be at least 85-90% efficient, so the input should be less than 360 watts for a 12 volt, 20 amp charger. At 120 volts, 360 watts is 3 amps. Even a tiny 18 awg or 16 awg extension cord will be more than sufficient for that small amount of power.

As to the charger, I'd keep looking. The one you linked would indeed charge at 20 amps (max), but there are newer rules about battery chargers that prevent newer models from charging batteries too quickly. This has much more to do with inexperienced consumers charging cheap car batteries way too fast, the batteries giving off a lot of hydrogen gas, and fires/explosions happening. The charger you linked isn't for continuous or regular use; it's more for occasional use.

I'm retrofitting an older RV, and I'm probably going to go with one of these models. The advantages are automatic charging, mounting ability, and it's a constant-duty unit. It will provide 12 volts DC while charging your batteries, so you can run your house lighting/accessories while plugged in at a camping site.

I'd also look into solar panels. You can easily fit 500 watts of solar panels (about 3 x 6 feet, give or take a bit) on the roof of a van, and 300 watts is 25 amps at 12 volts. That's likely more than you'll draw at any given moment (unless you're running a microwave oven), and it's a one-time purchase that gives you free power almost anywhere for a couple decades. It can get pricey - a 300 watt solar panel and charge controller will cost around $500. I'm looking at something lie this setup, but I might go bigger. I have a 32' Class A, so roof space for solar panels is abundant - if only money was...lol