I know that this is hard on you - mentally! I bet you will be exhausted after today. It sounds like ACAT is doing their darndest to get MIL in respite and to keep her in a NH!! I will keep my fingers and toes crossed for you.
And they are really looking out for you too. I think that they can tell from your voice, that you are about to give out!!! If I were you, I would not call FIL until she is in the NH.
I think that is interesting that the Adult Day Care did not tell you about MILs doings - like wandering and not getting along. Do you think they told BIL and he just did not want to inform you? Oh well - it sounds like this respite came at a very good time! Maybe the ball will be kept rolling!!!
Take care and rest, rest, rest. Also relax and sleep. :>