1.A 首先：选On是对的,在早晨：In the morning
但是在具体的某天早晨,就要用On.英语里表示具体的某一天就要用On.
第二个选项：注意一个动词show,它后面可以接双宾语：如：show me （间接宾语）a picture（直接宾语）.
注意这段话：（来自语法书）有些动词接间接宾语时,把间接宾语放到后面去,不过其前面要加to,这类动词有 accord advance award bring deal forward give grant band lease lend loan mail offer owe pass pay play post read rent repay sell send serve show sing take teach tell write 等.
所以就改为：show a picture to me.
你的文中是 show their mourning to joe 也可说成 show joe their mourning.
那么什么情况下用for呢?（来自语法书）
有一些动词,也可以接双宾语,但把间接宾语放在后面时,要改由for引导的短语,这类动词有 book bring build buy cook cut design fetch find fix get leave make mix order paint pick play prepare reserve save set sing spare 等
2.A move+someplace 年月前用in 而上一天是具体的某年某月某日所以要用on