Hello Chloe, recently my friend got a job in Barbados and is moving to Barbados. She asked me (since I live in Barbados)Â to look at some places for her and send her photos, this is how I came across this blog. Ironically enough her preferences were similar to yours, except she has a smaller family but everything else applies, she wants the real Barbadian island living not too far from the beach. I have been searching and was quite impressed with places such as Emerald Beach, Claridges, and St. Peter's Bay.
She really seemed to like Claridges from the pictures online. Hopes this helps to narrow your search down. Thought it was funny that you guys had similar preferences.
Best of Luck!
Alba