The Brown often have their windown cleaned by a young cleaner. (正确)
have sth done 结构后面是可以加 by ... 短语的。如:
We ought to have her examined by a doctor. 我们应当让她找医生给检查一下。(摘自赵振才:《英语常见问题解答大词典》增订版第五版p.599)
Last week we had all our windows broken by hooligans. 上星期我们所有的窗户都被小流氓打破了。(摘自《薄冰英语惯用法词典》p.371)