The sense seems to be:

Les yeux de l’enfant roulent des larmes.

So it’s a direct object, like ‘rouler une cigarette’.

For ‘rouler du cul’ (same for ‘des hanches’), the meaning is ‘from the ass’, not ‘some ass’. Like ‘puer du cul’, ‘grossir du cul’, ‘saigner du cul’. I think, that’s how I’ve always understood it. Now that I’m trying to explain it, I’m doubting…

It’s a direct object. Tear are rolling, and not rolled, even in French.

For your other problem expressions:

rouler des cigarettes

Here you are right, it means “to roll several cigarettes”

rouler des fesses
rouler des hanches

Both these means you have a specific way of moving that makes your butt do a rolling movement. Here it is equivalent to “de les”.

rouler des mécaniques

Here “mécaniques” is a slang for “muscles”, so it means “to flex”. It is the same construction as “rouler des hanches”.