Saw this last night and have been thinking about it with some disturbance ever since! It would be very distressing for your baby and 100 times more so for you for this to happen in the first few weeks, however sore and sleep deprived you may be.
Aside from anything else, if your area is reasonably well resourced for post natal care, you will be having a number of necessary visits in those weeks - health visitors, heel prick tests, checks on your health. They'll tell you roughly which days they will come, but not what time as it all depends, so you will find yourself needing to stay home for 99 percent of the time. And they'll kind of expect to be able to see and check on the babe, won't they?!!
What you might want to do is talk this through with your midwife, who I am sure will veto the idea, and then offer to take your SIL to another appointment with her, so that you can then bring up the subject and let the midwife back you up with matronly firmess on the no front.
I was also wryly amused about your DP: "And yes, I am planning to try and BF but DP just suggested expressing ...."
Oh, right, so that's all there is to it? You can just pump a few fluid oz into a bottle when you get a minute before bed, and then get on with the dinner and cleaning the bathroom while humming La Traviata?!!! Sorry, I don't wish to be too facetious but even when it works brilliantly, breastfeeding in the early days is pretty hard for all involved, including your DP. Personally I think it takes about 5-6 weeks even for the baby to get its brand new digestive system sorted out to any degree. Enjoy the Infacol period and the Infacol face! Especially in the first days, you are unlikely to be able to express anywhere near enough on top of providing feeds directly as well, and both expressing and feeds take more time than you think.
That said, good luck and make a point of acknowledging to yourself when you have had a good feed, as even if you think it is all going badly, you will notice that there are good bits and progress, and this really helps. But don't get forced into doing anything you are uncomfortable with in terms of handing over your precious baby - you may also be surprised at the 'lioness streak' that motherhood will bless you with as well!