Windy lake, want family sailboat
For stability with the kids, I was going to suggest an Ideal 18, but with that much breeze you might be overpowered often, and the keel could make launching and hauling out an adventure on such a small lake. A Lightning would be big enough for the family and still provide some performance for you, but again, the sail area might be too much until the children get bigger, to help hold it down. Rhodes 19''s or O''Day Daysailors might be good options for you. They''re quite stable, (difficult to capsize, have good sized cockpits, and also cuddies, in case someone needs to get out of the sun or wind.