This is a very common issue, and one that has been discussed many times in the forums. Usually in the context of someone who has a motion sensor which controls the lighting, but then they want things to happen differently if someone uses the switch on the wall. Yours is essentially the same case.
The most popular way to handle this is to use webcore. Setup is somewhat complicated, but there are lots of people who will be willing to help you.
Want you have web core set up, you probably won’t need to use any other smartapps, it can pretty much do it all. 
( The other way to do this is to have the button change the mode, but the problem with that is you can only have one mode at a time and if you decide you want to do something similar in another room or if you have more than one person living in the house it just doesn’t work very well. Webcore, on the other hand, can handle pretty much any combination of stacked conditioners that you can think of. So I would just go straight to That. )