Not sure I can be of much help to you but you have just helped me a great deal with what to buy my DS for Christmas👍😊
I have not heard of these before but, from having a quick look based on Amazon reviews, I'm leaning towards the first one (Sky Lite). I think the projected image looks clearer/sharper. There seems to be a bit of an issue with the remote on the second link although it does have the benefit that you can play music through it via Bluetooth (I'm not sure my DS would use this feature but your DD might?)
Will watch thread with interest to see if anyone has any first hand experience.