Hey NewbieMom, our chatter this morning reminded me that I didn't get around to replying to your question. (I've been quite busy IRL so haven't been able to keep up on the DIS or reddit.)
I've never stayed at the Hilton Hawaiian Village, but I've visited the property many times and my BIL's parents have a timeshare so their entire family spends a few days every summer there with all the kids and grandkids.
Firstly, I don't think it should be a problem accommodating a family of 5, with 3 young kids. I've found most Waikiki hotels are very happy to accommodate "keiki." Just call the resort's reservations desk to run it by them before booking and just book a room for 2 adults/2 kids if the room occupancy is 4, then notify the reservations desk about the additional child prior to arrival. As a Diamond member, they may even upgrade you to a larger room or suite at check in. Typically if you request rollaway beds or a crib, those incur an extra fee.
The Hilton Hawaiian Village is kind of at the entry to Waikiki, situated at some wide and busy crossroads. It's like a 5 minutes drive to the Ala Moana Shopping Center, which has a lot of high end shops, a
Disney Store with some Hawaii exclusives, and a LOT of food court/quick service dining options and a Foodland supermarket that'll probably be cheaper than dining onsite. Waikiki's main drag of Kalakaua Avenue is about a 5-10 minute walk away. The Hilton Hawaiian Village property is massive, and once you're onsite you don't really feel the hustle and bustle outside. The property is lush, with koi ponds, a lagoon, several pools, and is situated on its own stretch of beach. My sister and BIL's kids love all the pools, and I think your kids would enjoy it too. I think there's a kids club for older kids, but your kids may be too young for that. There are also fireworks every Friday night over the beach at the Hilton Hawaiian Village.
I don't think it's a bad way to use a Free Weekend Night Certificate! Just keep in mind that standard rooms don't cost that much in cash during the off seasons -- typically under $300/night, but that $50/night resort fee (ouch) on cash bookings. I know some people like to use their free night at some obscenely expensive hotel, but having young kids makes that a little more challenging. On points, standard rooms go for 60k Hilton points/night with no resort fees, but again as a Diamond member you can hope for a nice upgrade. Booking with Hilton points also gets you a 5th night free. Also keep in mind the Hilton Hawaiian Village is included on Hilton's list of resorts where you can use the Aspire's $250 resort credit. That should help with things like parking and onsite dining.