Specifically here, I'm thinking of children' rights and interests, but also the broader sense of both. We talk quite a bit about children' rights, although ironically the US is one of the few developed nations that has yet to sign the UN's Convention on the Rights of the Child (but you can help change that here), and some groups have even started talking about the rights of the unborn lately. I don't think that's a healthy place to go, personally, to consider the "rights" of the unborn, because they are dependent on another person at that point, so you'd have two competing sets of rights and you would essentially have to place a value on one over the other- and valuing people in a hierarchical way leads to bad things.
We can however speak of the interests of children before they are born, in part because interests don't have the same moral imperative- generally speaking- as rights. It is in the best interests of a child that they be taken care of by someone with whom they have a close relationship already and not to be sent to a stranger for eight hours a day, but a child simply has a right to be cared for by competent adult(s) who will not be negligent of the child while they are watching them, for one example. Rights are inalienable, interests are not.
Approximately half of all pregnancies in the US are unplanned, so I'm willing to bet that in about half of all US pregnancies no one has considered the best interests of a child until the pregnancy is underway. It's not a question tons of people think about before they have kids- "Is bringing a child into this situation in the child's best interest?" Often, the question is framed from the parents' point of view- "Is now a good time to have a child?" Maybe it's a subtle difference, but it is a difference, and there are definitely times when this distinction could lead to very different answers.
Specifically, in the case of balancing time and money. When one has the time for children, one may not have the money for children, and vice versa. Children need both, and a lot of each. As a society, we tend to say that the first scenario (time but not money) is a bad thing. We talk about children having more children to more greatly benefit from social services, or that a financially strapped couple "should have waited" and so on. The second case (money but not time), we tend to brush off as not a problem. The parent will hire a nanny, take extended leave, whatever, but the presence of money makes the scenario perfectly alright. As a society, we ignore the fact that both scenarios lead to stress. Financial stress in the first case, but time stress in the second. In either case, the child is being brought into the life of a parent or parents who are going to be under stress before the child is born. Is that in the best interests of any child?
And more importantly, is it in the best interests of our society to essentially value the lives and families of the rich more than the poor? If children of lower class families are worthy of our scrutiny concerning whether or not their parents made the right choice, aren't the children of the upper class worthy of the same scrutiny? Conversely, aren't both families equally worthy of us butting out of their parent's business so long as the children are happy, healthy and well-loved? In the US, money most definitely buys added rights, it seems.