How can I make over the top of this coffee table to be more usable?

Use plexiglass instead of glass for safety reasons. It will not be quite as clear as glass but it will be safer for your grandbabies. You should be able to take out the entire window frame and take it to a local glass shop and they can do it for you quickly.

Plexiglass

Plexiglass is a great easy fix, but if you want the storage section not to show any longer, go to your stone/marble guy for a scrap piece and have them cut it to the size of the top. You can always remove it again when the mood for change strikes again.

You can also use a piece of plywood. Plexiglass is expensive and you would need at least 1/4" for safety.

Of course theyt gravitate towards it because they are being told don't touch I agree the plexiglass that way it's safe and they can be as curious as they need to be. Going to have to add a lock so once they do figure out opening & closing help prevent getting fingers smashed.

I think you should replace the glass with a wood top. The children like it (glass or plexiglass) because the contents look interesting to them. . .it could be any contents. . . it is the "secret" of them. When they are grown you can switch back if you choose.

Remove the glass and replace with 1/4" plywood. Not over the whole top.

I would remove the entire glass top and store it for future use. Then make a wood top, stressed like the rest of the table to match.