My daughter’s bike makes this horrendous squealing sound every time she applies either hand brake.

You need to ‘toe-in’ the brake pads. Easiest way to do this is to loosen off the brake pad, put a credit card or something of a similar thickness in between the pad and rim, but only at the back, so that the back of the pad is lifted slightly more from the rim than the front of the pad. Hold the brakes in, and tighten it up, then do the other side.

You definitely hit it with wd40 😅

If it’s not toe-in then there’s play in the calipers. Squealing is vibrations.

This is common with front brake, you get resonance when the pads hit the flat surface – imagine they “bite in”, but then the “system” around vibrates and it loosens, that stops the vibrations and it bites back in, which causes it again.

This is a V-brake (you can go look up these terms on e.g. YouTube tutorials setup), so you do not need to worry about having flex in the fork itself as much, but you need to eliminate the feedback loop. So look for anything loose in the setup, tighten up the screws, check if the wheel bearings are not worn out, I would even check the headset.

Then the “toe-in” topic mentioned here before helps a lot (and you need to re-do it once in a while) – it influences how the pads end up (not so) flush on the rim surface. It helps because the V-brake itself is always (to some extent) loose even when all bolts are tight.

Last thing I would do – dishwasher detergent clean the rim and the pads, also maybe if the pads look very “shiny”, I would sandpaper them a bit. Then go on ride a bit and even if it initially squeaks, watch if it does not go away once there’s a bit of dust particles getting in (ride a mile or so).

Last option I would consider – swapping rear and front brakes and perhaps getting new pads alone. Different type. Sometimes it’s a combination of rim material + pad material + environment (e.g. wet is noisy, dry is not).