Just an idea, and not based on any personal experience, but I know that visitors to GC arrange private boat charters frequently for snorkeling, fishing, diving, sailing, dinner, cruising, etc..
When you are looking for an op to support your diving, also mention your interest in a half-day family charter to see if they can assist you. They might be willing to make a package deal if you purchase a charter and a multi-day dive package with them.
I recall that Red Sail used to offer a free Sunset Sail if you booked a dive package with them but I don't know if they still do that - but that's the idea. A dive op might offer their best price, or an extra perk, if you commit to a significant package purchased from the same op. Are any members of your family interested in a Discover Diving experience? That might also be part of the package.
Again don't wait too long to book because the dive ops will do their best to accommodate you as long as they are not already booked up with other commitments.
Also, if you are planning a major family outdoor excursion then consider booking it early in the week, so if you run into bad weather there may be time to rebook it later.
FYI, the month of May can be rainy but not always, and that is true over most areas of the Caribbean. Often it rains for awhile and then clears up and the sun comes out. And usually the winter winds calm down as you are heading into summer. Also, it is prior to the hottest air temps and before the start of the Hurricane Season. There's never any guarantee about the weather but May has potential for being great diving and a great family vacation.