In my own experience and what I gather from reading threads it is totally normal for milk to drop when you switch to a cup from a bottle. I think that's why some people choose to keep a bottle each day to keep the milk up, it does depend how much your LO is taking, for some it doesn't matter if the milk drops as they are getting more than enough, for others they need the milk not to drop too much. For my DS I worked out he would just about have his needs met with the smaller milk in the evening (sippy at supper time and cut the BT bottle) plus dairy solids (cheese), but that I needed his morning milk to stay up. DS appeared to know this himself because cutting the BT bottle was easy but switching the morning bottle to a cup was 'impossible'. For a couple of weeks I experimented with slit teats and sitting up straight (on my knee) for the morning bottle, tried a few times to switch it to a straw in a bottle which he didn't go for, then a couple of weeks later he accepted. I couldn't switch to a sippy cup as his milk would have dropped too much, with the straw he drank his full amount. BT bottle was ditched at 12 months, morning bottle switched to straw at 13 months.
Now, almost 2years on he has morning milk in a sippy cup (funny as all other drinks are in an open cup, but morning milk appears to have some comfort level in addition to calories) and he takes a full cup sometimes asking for more. So in time the level of drinking from a sippy *can* increase but maybe not as early as you need it to. He no longer has supper milk.
I personally wouldn't switch both bottles unless you find a way she will take a decent amount, maybe a straw? I used disposable straws (the fattish ones) as I didn't trust them to be 100% clean after milk being in them, so just rinsed them out and saved them for the crafts box.
hth