I'm being cruel to be kind here, your daughter is still well within the age range to suffer cot death!!
1) get rid of the cats or your daughter - personally I can't see a choice.
2) clean the house top to bottom side to side to get rid of cat hairs, dust, pollens etc, if you have carpet consider getting tiles or wooden floorboards as these are easier to clean & don't have anywhere to "hold" dust the way carpet does.
3) that's alot of medications for such a young child - talk to your dr about whether there's a way of reducing this. Also look into alternative medicines (you can do this on-line in a search engine just look up alternative or natural therapies or naturopathy, homeopathy, bowen therapy, accupressure, acupuncture to name just a few. A natural alternative might not only het her off so many meds but might also work better.
4) old wives tails!! The old remedies that were used before multi-national pharmaceutical companies came along & when drs were only for the rich & even then weren't always nearby. Camphor, eucalyptus & other similar oils can help ease breathing (you can also put them in a bowl of hot water & have the child breathe in the fumes, but I can't see a 2 y.O doing this!! But these oils (we here have vicks vapor rub) can be rubbed on their chests, neck & back & under feet seems to be good too for some reason - this at night or you can putr it on their singlet if it's too strong to be on their skin.
5) physiotherapy works wonders if you do it enough & regularly, i'll rty & describe what you need to do - lay her over your knees (face down) then form your hands into like shallow cups & drum very firmly them on her back over her ribs first one side then the other preferably for 15-20 mins per side. This helps break up mucus. You repeat as often as possible & when she's coughing or seems likely to start.
6) encourage her to spit up any & all spit/mucus she coughs up also encourage her to learn to blow her nose, both get rid of mucus.
Your chest & throat could also benefit from vicks vapor rub (or camphor/eucalyptus oils rubbed on throat & chest & around ribs (back & front) also the breathing over hot water with some ofthe rubs in it & a towel over your head - if you get stuffed up.