I personally wouldn't stay on the Palm. Its a complete nightmare to get off.
We go to Dubai every 6 months or so since DS2 was 2. We always stay at the same hotel-Le Meridien Mina Seyahi. Its a small hotel by Dubai standards (although 5*). Its near the Marina. The staff are fantastic and it's lovely for children.
Stayed on Palm last year at Anantara, which was fantastic (just past your two choices) and didnt have any problems getting on and off The Palm. Obviously it you want to go to various attractions on the mainland then it's less convenient however we enjoyed the relaxing beach, (very calm sea being protected from the ocean, ideal for young ones) and the views from The Palm.
Thanks for the replies, very interesting to read people's varying experiences! Unfortunately I am no longer pregnant so we can fly further afield, but want to stay away from Zika so we're going to the Seychelles Will look back at the advice for our next holiday though, thanks!