Just FYI, You can't use 2 days on the same day. The turnstile will not allow it. You can only use one day at a time
No you would not be able to do that because it technically would be park hopping which, if I am reading correctly your mom will not have. If you want to use the EMH and you do not have park hopping on your tickets that would have to be the park that you spend the whole day in.