Hi Disneynuts! Sorry to hear about your daughter, I know just what it's like to travel with a little one with allergy/asthma issues. Sadly, I know about it all too well. Two of my four sons have moderately severe issues and our fourth son has very severe issues. You picked a great place to vacation though! Disney has been the most accommodating company as far as our special needs (even above the Ritz and other luxury resorts).
First a question for you, has your reservation been 'blocked out' by special services? If not call back and get whatever reservations CM you talk with to call special services and have your special cleaning noted as a medical NEED not just a request. Maybe you already have this done.
In that case, call a reservations agent and ask that they have special services note the needs you stated above on your reservation. If a request comes through from special services instead of just one you make it carries a LOT more weight. I wouldn't try and request a specific long house or location. I would tell them what you need and why and then leave it up to the room assignor to pick which area they know has the least vegetation.
In the past, I have also talked with them (special services) myself and asked them to transfer me to a housekeeping supervisor at the resort and explained our allergy/asthma triggers to them so that we could work out what parts of the VIP cleaning were essential for my son and which ones were okay for them to skip (for instance, we don't need his bed linens/towels washed separately without detergent). Also, I have been transferred to the resort's room assignor by mousekeeping in order to discuss room requests. Trust me, the housekeeping at the resort does NOT want you to request a move!

Doing a VIP cleaning requires a LOT more work on their part to get a room ready for incoming guests. They do NOT want to have to do that work again should you come in and request a room change. They would much rather have your requests noted beforehand and be able to provide you with what you have requested if it is at all possible in the first place.
Anyway, in the past, I have always had great luck with our requests. Still, I know they are just requests and as long as they guarantee the medical needs, I will happily take whatever else comes to me by way of room location. I know that having medical issues doesn't make our family any more deserving of getting a request granted than anyone else's but at the same time, I think that the resorts have been great with recognizing that my family (and others with these severe issues) don't really have the latitude to ask for last minute changes or make last minute requests and offer to wait so they can be fulfilled (like most others who could ask that they be given a third floor room at check in and offer to wait until the next one becomes available vs. taking the first available room which might be on the first floor).
That said, in our case, what is outside our window would have no impact on our son's condition so I don't feel we have the right to request a room change for anything less than something major broken, leaking or otherwise untenable conditions in the room since I know the amount of work they would have put in ahead of time. In your case, however, I WOULD request that change even if it meant them doing all of the extra work over again if it was my child's health at stake.
I know you didn't ask any of that, but instead of faxing a room request or calling reservations and adding requests, I would deal with special services to ensure that the medical needs are noted with them vs. just being considered a request. Once special services sends your medical request to the resort, your room will be dealt with BEFORE other room assignments. If your request is based solely on medical need it is given a lot of weight and if at all possible, it is accommodated and is blocked ahead of time.
Cleaning starts almost always before you even arrive and in some cases before you even leave home- they like to give themselves a cushion of a night for the in depth cleaning if at all possible depending on how busy the resort is when you visit. The room you end up in is not even in the general pool of rooms available to other incoming guests. Again, they aren't going to put in all of that extra work and then hand it over to somebody else who doesn't require the extra effort to occupy a room and then have to do it all over again for your party.
Hope this helped (I wish someone had explained this all to me back when we first experienced a need for this type of help, I learned as we went on vacations over the years by talking to some great CMs at different resorts mousekeeping departments, special services and even a few resort managers). If you knew all of this already, SORRY!! I didn't' mean to sound preachy or like you didn't know what was going on. And as a disclaimer, I am not a Disney employee, this is just what I have been told and how things have worked for us in the past (as recently as this past March).
Have a great vacation! I cannot wait until our stay at the Poly (about 45 days out for me).