I am a law school graduate. What I offer is mere information, not to be construed as forming an attorney client relationship.
You didn't give us your state but here is my take:
yes it can be used against him because the fact he drinks and the fact he got a dui and was convicted of manslaughter shows there is a possibility of endangering his child. Child endangerment allegations are taken quite seriously in custody cases.
As for dui and manslaughter, dui can be the catalyst for manslaughter:
Manslaughter:
manslaughter
['man-'slô-ter]
: the unlawful killing of a human being without malice
(compare homicide murder)
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involuntary manslaughter
: manslaughter resulting from the failure to perform a legal duty expressly required to safeguard human life, from the commission of an unlawful act not amounting to a felony, or from the commission of a lawful act involving a risk of injury or death that is done in an unlawful, reckless, or grossly negligent manner
(see also reckless homicide at homicide)
Note: The exact formulation of the elements of involuntary manslaughter vary from state to state esp. with regard to the level of negligence required. In states that grade manslaughter by degrees, involuntary manslaughter is usu. graded as a second- or third-degree offense.
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misdemeanor-manslaughter
: involuntary manslaughter occurring during the commission of a misdemeanor
(compare felony murder at murder)
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voluntary manslaughter
: manslaughter resulting from an intentional act done without malice or premeditation and while in the heat of passion or on sudden provocation
Note: In states that grade manslaughter by degrees, voluntary manslaughter is usu. a first-degree offense.
DUI might be a lesser included offense, if it is, one cannot be convicted for both.