You should use the light meter in reflected mode near enough to your hand so that it only reads your hand. Your Gossen light meter should have written on it the angle of view it measures (It's a small "V" with a number such as 20°near it). If you don't find it, look in the instruction manual to see which is the measuring angle in reflected light mode.
Generally speaking when using a light meter one should be careful not to project a shadow (with the hand, or with the body) on the thing measured. In this case we assume the sun is somehow in front of you so there is not this particular risk.
If you don't want to disappoint your family, I'd avoid backlit situation. "Put the sun" at your shoulder, you'll have much more light and you'll be able to use a much closer aperture so as to be sure to have running children in focus.
If the sand is bright and the sun is high you can probably use, with ISO 100, 1/125@16 or even 1/250@16. That should be enough to "zone focus" and only concentrate on the subject.
Beware of the sand and of salted water, that's VERY bad for any equipment. The seaside is exactly the place where I would bring a disposable camera and be relaxed.