Famous quote from Charlie Papazian, the king of homebrew and founder of the American Homebrew Association: "Relax, Don't Worry, Have a HomeBrew!"
It's general brewing advice; don't worry about it, it'll be fine! Someone once told me that wert WANTS to become beer. It's difficult to prevent it from doing so. Same goes for wine, cider, mead, or whatever other delicious alcoholic beverage you are creating. Once you have sugar in a solution and add yeast, it's extremely hard to stop it from becoming a delicious fermented beverage. You may get some different flavors from all of the temperature changes, but once you bottle that sucker up and try your first sip of this incredible substance you have created, you will realize that the whole process is not nearly as complicated as you once thought.
Having said that, here are some things to remember:
1. You must get some type of sanitizer! StarSan is my personal favorite. In a pinch, fill a 5 gallon bucket with water, add 1 tsp of bleach, THEN 1 tsp of white vinegar, and VOILA you have a bucket of sanitizer for ~$.02. (NOTE: DO NOT add the vinegar and bleach together first, this will kill you. Literally.)
2. When those yeast suckers are taking off, and the alcohol levels are rising in that cider, you really have very little to worry about in the way of infecting it. It sounds like you're soaking every object in your house with alcohol - certainly unnecessary, trust me. People on here can tell you stories about dropping things/dunking their whole arm into a wert or must and having it ferment without any problems. One guy even used a spoon in his beer that had all over his dog's butt not 5 minutes earlier. I'd still of course advocate for sanitary practices, and you should still sanitize everything that touches or comes close to your stuff just to be safe, but it's not an area to freak out about too much.
3. If you can't rig that blowoff tube, keep doing what you're doing. If the airlock keeps filling up with cider, keep emptying it and filling it with sanitizer or vodka. Next time, get a blowoff, or brew slightly less cider in your carboy. You can also try using a champagne or wine yeast, which should create less krausen (that thick bubbly layer) while fermenting.
Good Luck!