I have only been to HHI, so I can't speak to Vero. Since you will be traveling with two little ones I would highly recommend HHI. It has a very wide beach, and the surf generally is pretty calm, good for little ones. The beach house is awesome providing the pool, quick service meals, snacks, smoothies and drinks. There is also an air conditioned room room at the beach house with tables, couches and a TV if you need to relax out and want to get out of the heat. Not the most comfy place to hang out, but sometimes a welcome place to spend a little time of the sun and heat are getting to you. At the resort itself there is also a pool and various activities you can sign up for.
To get to the beach you will have to drive (plan to be there by 9:30/10:00am to ensure a spot. Or take the bus -- which runs about every 20 min. I'm not sure what time it starts running -- I want to say 8:00am and service ends at 5:00pm. After 5 you would have to call a different service for a ride. There is no charge, but it can be a l-o-n-g wait to get a ride.
At the beach I highly recommend water shoes. There can be stingrays in the water and shuffling your feet as you enter is always a good idea. In 5 years I have not seen a stingray, but I have heard of people being stung when they aren't careful -- hence the reason for the water shoes to help protect your feet from being stung.
There are a total of 97 two bedrooms at HHI. 76 are dedicated two bedrooms and 21 are lock-offs. Be aware that the buildings at HHI are spread out on the property. Only the Live Oak Lodge and the building attached/next to the Live Oak Lodge has an elevator. The vast majority of the 2 bdrm lock-offs are in this building. If you end up with a dedicated two bdrm, but be aware that you will probably be in a building without an elevator. I'm not sure how hard it is to book a 2 bdrm in the 7 month window, but this is premium season for HHI and I can tell you that things do sell out quickly in the various room categories. Obviously, 4th of July is a difficult date to travel over, but I have successfully booked this timeframe at the 7 month window for a studio.
I own at HHI and take an annual trip there at the end of June - through the second week of July. I really really love this property! If you go have fun!
Hope that helps