We faced a similar choice when I first started planning our trip. Kids ages 5, 3 and 19 mo. Where to stay?
We basically made our choice by deciding that, with the money we would save by staying offsite, we could take another trip, perhaps even a trip each year, instead of every 2 years! For us, the extra money just wasn't worth it - my eldest really wouldn't even notice any of the 'disney' touches - he's actually just excited to stay in a hotel (never happens with us!)
We may consider the DLH or another DLR hotel when the kids are all old enough to appreciate it, however, I doubt it. For me, the extra cost just wasn't worth it, but this isn't a 'once in a lifetime' experience for us - hopefully just the first of many DL vacations!
Having said that, if you really have your heart set on the DLH, it may be enough to taint the whole vacation for you if you "settle" for the Desert Inn - they are in two seperate classes of hotel, from what I can tell. (haven't stayed at either) Make sure, in your heart, you are happy with whatever choice you make, and you will have a fabulous time no matter where you stay!! And honestly, your DD will probably be so excited to be there you could pitch a tent in the parking lot and she'd be just as happy!
Good luck!