I know I have said it twice already, but your best chance of getting into Kellett is a Corporate Debenture, which your husband's employer needs to fund. However they are not cheap, so they may not be willing to do so.
Aside from debenture status, the main requirement for Kellett is that your daughter speaks, reads and writes good English (for her age), but obviously you should include any other factors that may help her application on the form, such as her French (which is taught at Kellett, but of course the main second language is Mandarin). Once a place comes up, they will want to see that your daughter is at least as able as other children of her age, ideally above average. All schools in HK like to see a high degree of parental support - some schools check out the parents more intensively than the children, but Kellett isn't quite so full on with that.
Agree with OP that a serviced apartment should be for weeks rather than months. Many of them are only studios/one beds and the decent two bedroom places are expensive. We rented a two-bed at Taikoo Place Apartments for two months while waiting for our furniture to arrive from the UK and to give us some time to decide where we wanted to live longer term. The rent was in excess of HK$90k, even after my employer negotiated a discount. Pacific Place Apartments was even more expensive.