Do skinny women have more daughters? Do dominant women have more sons?

Yes on both.

Via Do Chocolate Lovers Have Sweeter Babies?: The Surprising Science of Pregnancy:

Researchers in Italy collected data on nearly ten thousand new mothers and found that those in the lightest twenty-fifth percentile — women who weighes 119 pounds or less before pregnancy regardless of height — gave birth to significantly more daughters than did women who weighed more (51 percent versus 47 to 48 percent in the higher quartiles.)

And:

…a team in Norway followed nearly forty thousand women during and after their pregnancies. They found that women with anorexia before pregnancy were 10 percent more likely to have daughters than average weight women. Those with bulimia were 9 percent more likely to have daughters.

And:

In this context, it’s not sexist when Valeria Grant, an evolutionary psychologist at the University of Auckland and mother of four (boys), steps up and asserts that high maternal testosterone is linked with male babies… In the 1980’s she created a test to measure personality dominance… The more confident and assertive the woman, the higher she scored on the dominance test. The higher a woman scored in dominance, the more likely she was to have a boy, or all boys if she had more than one child.

And:

T. Manning, a biologist at the University of Liverpool, found that women (and men) who were exposed to high levels of testosterone in the womb are more likely to have sons.