It was called
"A history of childhood: children and childhood in the West from medieval to modern times". Sadly the first 50 or so pages weren't included on Google Books, and they look like they might be the most useful. "Coping with Death" on p58 may well be worth a read though. Gives some basic mortality rates for the 17th

century.
I've finally had a chance to look it over, and there is some interesting stuff here. On childhood mortality, it is difficult to pin down numbers that would be acceptable for a game like this one. I would venture that 250 per thousand would not be a bad number to follow, maybe 300. It might depend on the region too. For the nobility, I would not say that it should be that different from the rest of the population, unless there is some data to argue otherwise.
This book also brings out some interesting information on grieving, illegitimacy, fertility treatments (eat more carrots, milord

), etc. that might be useful if you want to make your character's family life more interesting. There should be events, for example, allowing you to boost your character's fertility by way of herbal or sacred cures; mourning over dead family members (though the tension was between death being God's will and showing affection, and there were public vs. private signs of mourning); and so on.
What this author says about illegitimacy reflects what I know about the early modern era, that it depended on circumstances and time and place. Before the XII century, bastards were more easily accepted into the family, but this should not be a hard rule, either. Then there were important distinctions between kinds of illegitimate children: there were "natural children" produced between two unmarried people who could, in many places, legitimize their offspring by marriage. Thus, in William of Normandy's case, his father Robert was unmarried and could have conceivably married the mother of his son. It was a different matter if the father was married to another woman; there was more stigma attached to such children, who I would describe as proper bastards. Then there were other cases like the children of priests after clerical celibacy became the rule of the day: in Spanish these became known as "sacriligios" to denote that their existence owed to transgressing the sacred. So some food for thought.