Hi Alexfan,
What the weather is going to be like, is a very hard question. However, we have been quite a few times to Menorca in October and have always encounted lovely weather.
We normally go twice a year in May or June and September or October. It can be fantastic weather during the day and get quite nippy in the evening, so take something to cover up.
The resorts Calan Blanes and Calan Forcat (now joined up almost into one resort) stay open until the 31st October. So you won't have any problem at all.
You'll have a fab time, I'm sure !
We are going to be there in just over a weeks time and I can't wait.
As you've got kids, you will have to try Restaurant Haiti in the center, they are brilliant with the children.
The Water Park will also be open, it's not the biggest one you have ever seen, but its fine for families with young children.