Any guesses on if the teacher perks will be available again at the DS hotels next year? Were folks able to apply them after booking for stays this year? Trying to decide now about booking doubletree for our family of 5 for next June...
Using archive.org (aka the Internet Wayback Machine), I looked at saw that the teacher's discount was offered in 2016, 2017, and again this year. Based on that, I'd guess that it will probably be offered next year.
As far as reservation modifications go, all major chain hotels require a room to be available in order to make a change. So, if a room is available at the discount rate when you make the modification, you won't have a problem. If there's not a room available, the modification will not be allowed. It doesn't matter that you are holding a room for your dates. (I've never come up with a good way to explain this concept. If this doesn't make sense, let me know and I'll try again.)
When it comes to the question of whether a hotel will offer a discount, there are two set-ups. In the first one, a hotel will offer a certain number of discounted rooms each night. In that scenario, the fact that you (or other people) already have a reservation won't make a difference. Once you see that the teacher's discount is available, you can (hopefully) modify your reservation and grab the discount.
In the other set-up, a hotel will only offer discounted rooms on dates when their software says they need help to sell out. After all, there's not much reason to offer a discount if you can fill the hotel at the "normal" rate. In that scenario, the fact that you (and other people) are holding a room at the normal rate makes it less likely that the hotel will offer a discount.
I spent over a decade working in hospitality, including a big stretch as a Revenue Manager. The Revenue Manager is the person responsible for getting the most rooms at the highest rates every day. (i.e. all this stuff) Every hotel I worked at or knew about from colleagues used the second method of discounting.
That said, it's impossible to know if booking one room is going to be the tipping point for whether a discount will be available on your dates. Given that you're a family of five and that limits your choices (without getting 2 rooms), I'd go ahead and book the DoubleTree Suites...provided the rate is something reasonable. Then, periodically check for discounts. If you haven't, sign up for MouseSavers, as they occasionally provide discounts at the DoubleTree Suites. Also, check the Disney Springs Hotels website for any discounts beyond the Teacher's one.
I just threw out a ton of information. Feel to ask for clarification if something doesn't make sense.