Millie wants her mother【to come 】to Sunshine Middle School on the Open Day,
to come to Sunshine Middle School on the Open Day 是不定式短语做宾补的
在此句中,to come 不可缺.因为英语中没有want sb to + 名词（代词）这个句型
句型为：
want sb to do sth 想要某人做某事