Changing part time working hours

Hi, I need some advice on changing the number of hours I work. I currently work 16-18 hours over three short days. My mother looks after my dd one day a week, and dd goes to nursery for the other days I work. My mother will be going away for a number of months at the end of January, so I will have to change my childcare arrangements. The nursery may not have any extra places, and I would like to do two full days, instead, on the days dd attends nursery. I would also prefer to do two days, as the travelling is proving tiresome on occasions.

My manager was quite strict on asking me to be in the office 3 days a week, when I initially started. Now there are more people (but not doing a similar job), I am hoping this may change. My job is a bit difficult to do from home, due to client files, answering office phone calls and receiving/answering postal correspondence.

Does anyone think it may be possible to work from home for a few hours each week, in consideration of the above circumstances? What points should I raise when I speak with my manager, to help it going my favour, and to make it work from her perspective?

Any ideas would be helpful. Thanks.