Should I be worried about sand in the chain?
It was the right thing to use the lube for the chain.

I do not know the particular product but in general spray lubes have the tendency to become too plentiful on the outside of the chain. This film of lube will become sticky as the solvents in the spray are dissolved.

The grinding noise from the drive train may come from sand or grit sticking to the outside of the chain. The fix is to remove it. You do not have to use the more complicated methods meant for bikes where drive train efficiency and longevity are important.

If you have a degreaser or a light oil like WD-40 at hand it helps to soften the old lube. Otherwise use warm water with dish washing detergent. Spray the degreaser or light oil on the chain. A stick is often useful to scrape off old dirt and grease from sprockets and chain ring. Use an old brush or an old rag with the soapy water to clean off old lube (and detergents). That doesn't have to be super thorough. Rinse with clear water.

When you cleaned the chain this way, apply your 'Krown' spray lube again. Spin the gears or let your child ride a few rounds on your yard (not through dirt) to work the lube into the rollers. Then wipe off excess lube from the chain. Do this last part quickly after applying, while the spray on your chain is still fluid. After a while the light oils in it will disappear and only the sticky lube will remain.

We want the lube inside the chain, between rollers, not on the outside where it attracts dirt and grit.

shortcut:

If you are in a hurry, it might be enough to spray the chain again with the 'Krown' lube you have. It will soften the grease on the chain. Then wipe it all off with a dirty rag. Wipe also the sprocket and chain ring. Be careful not to pinch your fingers!

This quick-and-dirty method will get grit into the chain rollers, and reduce their life. But for the use you describe, that will not matter.