Slavery and family life are not my area of expertise, but to answer your question generally: it depends. From the time of Augustus onwards, the emperors passed decrees that gave more rights to slaves, and correspondingly, restrictions on how their owners could treat them.

Depending on what purpose the slaves had been purchased for, they could have been treated very differently. If they were intended as household servants, for example, mothers and children might be kept together. Whereas if they were fieldworkers or slaves condemned to the mines (damnatio ad metalla), they (men especially) might be separated from their families. In general, slave owners had not only the power of life and death over their slaves, but (e.g. for men) they could also castrate them, or assign them a female companion to breed with, etc.

I'd recommend reading Columella's On Agriculture (book 1, chapters 8 and 9). Notice in particular where he talks about how if a female slave bore and reared a certain number of children, he would sometimes reward her, even to the point of giving her her freedom.