So it's not this exactly but I'm currently working as a research assistant in a personality/social psych lab. We're doing pretty novel study about parenthood's affect on moral judgment and relationship with political conservatism.

So we theorized that parents would tend to score higher on the "binding" aspects morality tests, meaning they judge the moral foundations of loyalty, authority, and sanctity/purity (meaning in our context, digust with "impure" actions concerning food or sex). Nonparents were expected to score higher on individualizing moral foundations (care, and fairness). Binding moral foundations are correlated with conservatism and typically match conservative values (for example, conservatives are more concerned with "sexual deviance and respect for those in power). The study uses tests for moral foundations and for social and economic conservatism and correlated it with parenthood (we also use a prime for the experimental rather than correlational aspect of the study but I won't get into that).

So what we've found so far, we've only had 3 trial as of yet, is that parents are more socially conservative and have make harsher moral judgements in general, with binding foundations being slightly harsher than individualizing. So although we don't have research about single mothers specifically, parents in general actually tend to be more conservative. There is actually much less research about the affects of parenthood on people than you would expect. Most of the research is focused on the children.

Anyway this study isn't published yet, I hope to be able to link you to the article sometime in 2018.

TLDR: The limited research says that parents in general are more conservative, so right now there is little evidence that single mothers differ, though that may change.