T.C.
I would do it as a Thank You party. Thank her for giving of herself to care for her father. You can then give gifts to show your appreciation of all she did... things to pamper herself (pedicure, massage and always chocolates lol)as she has done for her father would be appropriate. Also, some kind of memory book with pictures and then add some poems or stories of other people who give so much of themselves for others.
So, I would go but if they do not address it properly in the term they use for the party, just make sure you do so in your card.
Remind your BIL and family that she is going to go through a grieving process just as if she had lost him to death. That celebrating her freedom may not be the right choice of words for the party. She is going to constantly question if she made the right decision to put him in there. Her Father is also going to be going through some major changes and the Alzhiemers will show new forms- he will be very confused as to where he is and why he is there and may even regress further. This is going to be hard on her and make her even more regretful that she had to make this decision.
So, the only way to tactfully "celebrate" is to thank her for being the strong woman that she is, the one that raised her kids and has helped her Father! She is an amazing woman!
God bless you and your family! I will pray for your MIL and hubby to be able to come to terms with the decision that was made!