Think it is one thing expecting to muscle in on your childminder/babysitter for the evening, it is quite another thing to expect to stay over as well!
Is your house much closer to their party than their house making for a cheaper taxi ride afterwards?
I'd be very tempted to say 'sorry, I've booked cm/bs for the kids to have some time alone with her as they have been missing her individual attention so it's not convenient for her to look after your dc too. Here's the number for sitters/another babysitter'.
if you feel you can't turn down the babysitting bit, then you could say that she will babysit but that it isn't convenient for bil and sil to stay but that they can pick up their dc when they go home. Wouldn't offer overnighter for the dc without the parents there.
I would also speak to the cm/bs first and say that maybe when you spoke to her to arrange all this and made sure that sil wasn't booked with her for that night that maybe you'd all got your wires crossed and that you'd been talking at cross purposes and you were kind of upset as you actively wanted her to look after your dc without her looking after anybody else - nephew/other mindee/complete baby stranger/etc.
Say that you are upset that sil has approached her first and arranged it all with her without consulting you first because you would have never said yes to sil if she had asked you as your dc were looking forward to spending some time just with her.
Also ask here exactly how sil asked her to look after her dc - did she make it sound like you had already agreed to it - you never know there might be a thread lurking somewhere about cm/bs being hacked off that she had arranged to look after 2 kids and now has to look after 3 
- she might be hacked off by it too, or at least railroaded into it by sil.
Tricky part is knowing if sil has offered her money - if she turns sil down now then it might feel to her that she is turning down money. But if you are paying her over and above her normal rate then you could say that you thought that you were paying for her to just look after your two. And if sil isn't paying any extra then it is obvious that sil is a cheapskate for a separate rant...
I would also say to the cm/ds that you don't have the space for your sil/bil/nephew to stay and that quite frankly don't really feel comfortable with them staying there while you are not, it's not fair on cm/ds to have to look after kids and act as host in the morning as well.
agree with her that you are not happy with the arrangement and that you will take flak from sil if she gets shirty with cm/ds (she might not want to compromise her income and feel she is between rock and hard place if you both pay her and want different things).
before speaking to cm/bs remember to write all the points down that you want to cover and think up what you want to say in response to what she might say to you, so you have got all eventualities covered and don't get caught on the hop agreeing to something that you don't want.
then send text to sil just saying that you have spoken to cm/bs and asked her to revert to her original agreement with you of just looking after your dc, which she has agreed to, as 'for a number of reasons' it's not convenient for her to look after dn or for them to stay there after party.
If she can send you message like this by text then don't feel bad about replying by text either!
Good luck - and let us know how it all gets sorted out!