In my opinion I can't see the issue with you taking your DD. I can see your DP's point of view but I dont feel missing a week of school will cause much hassle. As stated by others you can always get school work for her to take along. Sure its not a holiday but your mum asked for your DD to go along and I think that if its what you would like to do there is nothing wrong with that. My granddad recently had a quadruple heart bypass, followed by multiple blood clots etc. One thing that keeps him smiling and brightens his day is me taking DD there.
Personally I don't see any issues with it and I think you just need to have a good chat to DP and work something out.
You can take the other two next visit or take another one next visit and rotate them.