There are several ways I can respond to this post. For one, your argument, and the question that follows, is based on the assumption that poor people have more offspring than wealthier people, to which my response is What is your proof? Perhaps in modern day society where contraception is prevalent wealthier families are having fewer children than poorer ones, who either lack the finances for or the education about contraceptive use. The following statement, "After all if people just want to propagate their genes and all our behaviours", is a common misconception of evolutionary psychology. Humans are often unaware of the evolutionary reasons behind the behaviours they engage in, that is, there is a qualitative difference between the motive and the purpose of a behaviour. Humans, particularly males, engage in sex not necessarily to propagate their genes or to produce offspring (although certainly some couples get together with the intention of having a child), but because they physically and emotionally enjoy sex (motive). The evolutionary reason that they enjoy sex (that is, the function of the behaviour ) is that natural selection has endowed them with such emotions so that they are motivated to engage in the behaviour, thus propagating the genes responsible for such proclivities, which is the goal of the "selfish" upon which natural/sexual selection exerts its pressure
But back to my original point, which was that this disparity between offspring produced by rich and poor families (assuming it's true) by no means suggests that males in wealthy families are not pursuing more extra marital affairs than less wealthier males. If a female does have an affair it is almost invariably with a wealthy, powerful, or high-status man, so it appears that wealthy men are capable of attracting more mates, and thus capable of producing more offspring (barring contraception), than poorer men. However, number of mates does not necessarily translate into number of offspring (females do not have estrus-physical cues that they are ovulating, which many primates, such as chimps, display). So the question you should be asking is not do poorer families have more children than rich, and if so, why, but rather, do males with more resources attract more mates which, barring contraception, would afford them more opportunities to produce offspring?
In the pleistone era, where we supposedly evolved, and the few hunter-gather societies that still exist today, the males with the most resources and highest status attract the most females, and, consequently generally have the healthiest offspring. (Also, throughout history dating back to the biblical ages and across various cultures, kings, emperors, political leaders, and the like often had hundreds, sometimes even thousands, of children.)
Another problem with your post is that you are conflating males and females sexual and reproductive interests. You speak of certain "families" having more children than other families, but a family is not a cohesive, unanimous group with common interests. It consists of two partners, a male and a female, who both have remarkably different sexual and reproductive interests. You are right in that males’ evolutionary goal-albeit they are often not conscious of it, or at least no more conscious than a frog is-is to propagate their genes which they do by inseminating as many females as possible. However, females do not benefit from such promiscuous behaviour, as they are the ones who have to bear the pregnancy for 9 months and then some. So the behaviour of each member of the family needs to be understood within the appropriate evolutionary context, and not just as a "family".
Now, onto to a theory which does take wealth into consideration when explaining human behaviour: A male is better able to monopolize being born into a wealthy family, that is, attract more mates and produce more offspring because females typically look for resources in a potential partner. Thus, we would expect parents to invest more time and resources in raising male children when they are living in good-i.e., wealthy- conditions, because males would be better able to translate those resources into mates, and, eventually, grandchildren. A female is limited in the number of offspring she can produce in her lifetime, something called reproductive value. But a male, given ample suxual opportunities, can produce pleny of offspring because he is not obligated to carry, give birth, and, in some cases, invest time.resources into raising children. Thus, the best way for wealthy parents to ensure they have plenty of grandchildren is to invest in their male children more than female. In fact, richer families beget more male children than poorer, who, in turn, beget more females. The explanation of this latter fidining is unknown, but several theories have been proposed.
In poorer conditions, however, we would expect the opposite to ring true. That is, parents would invest more time and resources in raising female children because they, of the two genders, are more likely to find a mate and produce grandchildren. A poor son is not a desirable mate, so he is less likely to attract a female with whom he can produce children. The saffer strategy for the parents in this situation is to invest more in their daughers.
So, contrary to what you mentioned above, evolutionary theories do offer predictions for the behaviour of the rich, not just the poor. You’ve just asked the wrong questions, and so have had difficulty finding the right answers.