Wow, thank you everyone so far...To answer a few questions above:

We are going for 6 nights. In and out of LIR.

I have a friend, US expat who lives there--I reached out to him last night and he replied how excited he is that we're coming...And he's going to set up activities (and bring his girls about the same age as ours), pick us up from the airport and put us in touch with his on-call driver for anything else we want to venture out for. So, unlike a lot of people, we have activities to keep us occupied when we're not swimming/beaching it and relaxing! He suggested the W, however--I see it's only not bookable because all (remaining, if not all rooms) are 1 king and a max capacity of 2...So that's why the W is out for us. The Westin appears to be adults only, as that is then only bookable if I remove the kids. So, unless I'm missing something, it's still the Mangroove or JW for us!

Again, I sincerely appreciate everyone's help so far and appreciate any further advice too!