Hi!
In regards to Tokyo Disney Sea, October is one of the peak months to visit and even with a full day, be aware you're not going to accomplish as much as you would think.
This is the crowd calendar:
http://www15.plala.or.jp/gcap/disney/It's usually pretty accurate though my last trip thanks to G20 my nice light blue day became yellow. The 15th is a cranberry day. There are likely to be capacity controls. You need to be there early, or you might not be getting in, you are not going to be getting in with a Twilight Ticket if that is what you had planned. I went once with a Twilight Ticket on an orange day, every ride had at least 40 minute+ lines including Sinbad. Just walking around was hard. It's a nice park, but unless you and your child just enjoy admiring the scenery of a theme park, go early, as early as possible. You could also move your visit to the 16th or 17th, though it will still be unpleasantly crowded just not ticket restrictions crowded (probably.)
Sea opens at 8:00 am when you are there. People will line up before 7:00 am for entry. It's going to take you a good hour from Shin-Egota just to get to Maihama and then you need to either walk or take the monorail.
Even getting in late, the jetlag from the US can be bad. Take advantage of it. I find it means I am up super early. Shrines like Meiji Jingu tend to open early vs. many shops which seem to open late. So your visit doesn't need to be that fast as nothing is really going to open in Harajuku before 10:00 am and some places will be even later. We got in about 8/20:00 this Summer to our hotel (because we transferred to Itami from Narita) and we got in after 10/22:00 last Summer to our hotel because we took the train between Tokyo and Osaka post arrival. It usually takes my child 1 week to adjust. I would not plan too much in the evening. I've done 4 mother-daughter trips to Japan.
Like everyone already said, don't get a rail pass. If you go to Kawaguchiko, you're getting outside of Tokyo. I think depending on what you are shopping for and your tolerance for shopping, you might be spending more time shopping than you think. Unlike many people on this forum, I am a shopper. My daughter and I collect Japanese fashion dolls and places like Nakano Broadway Mall you can spend a lot more time than you would think. I am surprised the Mandarake in Shibuya isn't on your list.
With $1000, you can spend about $140 per day on food, transport, shopping, and entertainment. Whether that is enough depends on what you plan to spend on those 4 categories.
In regards to Goshouin, you might want to try to do a search on what some of the books look like. I have a few Goshouin books, 2 have pretty boring covers, but the one at I started at Kushida jinja is quite impressive. (I had to ask a friend in Fukuoka to get one for her so we could have the same cover.)
Good luck!
Good luck!