GayDays is a convention, not sponsored by Walt Disney World, that takes place in Orlando on the dates you are planning to visit. The events take place all over the city, not just at the Walt Disney World theme parks.
The schedule for the GayDays events that take place at the Walt Disney World theme parks can be found in my answer
HERE . My suggestion for you would be avoid the theme parks on the days that are scheduled days for the convention crowd.
You will have to decide for your family if there will be a problem visiting Walt Disney World during this week. The conventioners you will encounter are likely to be families, much like your own, there to enjoy Walt Disney World. Any public displays of affection are probably going to be innocent, similar to what your own family might display. You know your children better than anyone else, so you will have to make the determination that best suits your family's situation.