I don't understand why you think it is a paradox. If a family is poor, without good health care for example, then more children will die or fail and it will hurt the family harder. Their employment is also more likely to be manual labor based where children quickly supplement their capabilities (e.g. farming, retail). It's simple economics.
"More resources -> less reproduction" has, to the best of my knowledge, one example in the entire animal kingdom: Us.
You're looking at the reasons, which are also interesting, but the next layer of abstraction down from the point I'm making. (Though I'm not sure you're not explaining why poor people have fewer (surviving) children, which is the opposite of the data....)
