You can look up the teacher discounts under 'special offers' on the SwanDolphin website. Go ahead and start to make a mock booking for your dates and you will see what the current offer is at the time you are looking. It is worthwhile to keep checking, as discounts seem to rise and fall over time. (I guess that is the 'floating' PP spoke of). The best deals seem to be offered for the standard rooms (no balcony or view) but if you join Starwood Preferred Guest, they will sometimes upgrade you one category at check in.
We haven't tried at Easter, but we have found that the best deals seem to be during times when Disney rates have been really high. For example, this Thanksgiving my DIL (nurse rate, same as teacher) has a rate of $179 at the Dolphin, while the garden view at the Yacht club is $480 per night (I don't know YC standard view - it is sold out). That is a savings of more than 50%. Even we have a Balcony, Epcot fireworks view room (
AAA discount) over Thanksgiving for only $265 per night. Even adding on the $23 daily resort fee, those are great rates compared to Disney prices. We also get a resort credit of $50, which nearly covers the cost of the $60 cab ride back to the airport. Plus, unlike DME, the cab brings us to the airport when WE want to go and without other pick ups along the way
We LOVE staying at the Swan/Dolphin! They have the best beds in all of WDW, IMO. And an amazing location.
Good luck!
