这两句都对的.
1/ You can't expect her both to do housework and look after children.
分析:expect 谓语动词,后面接两个动词不定式 "to do housework and look after children" 很清楚的.若在 look after ...前加 to 就更好了,用 both 限定了这两个动词不定式.
2/ You can't expect him neither to smoke nor drink.
分析:谓语动词 expect 被否定,him 做宾语,用 连接词组 "neither to smoke nor drink" 连接两个动词不定式.意见同时面一样:在 nor 与 drink 之间加 "to" 更好些.