Yes you can definitely take family with you in May. The temperature would be good for kids also. According to Google stats it may vary from 16°C to 25°C. So keep 1-2 warm clothes if you're from Hotter areas than this atleast for kids.
Definitely it's worth to go to Sikkim with kids.. you have ample activities there along with nature. A day at nathulla pass would really be an icing on the cake for the kids as they get along with the army officials there and see the indo china border. Tsogmo lake and the yak ride there would be memorable..you have activities like ziplining,river crossing river rafting and many more at the tourist spot there.You can also have a visit to the miniature of Char dham there. if you can add North sikkim in your itenary, it's a bliss.. but the travel time is more.View from paragliding is breathtaking.MG road is a lane where vehicles are not allowed, so kids can come in the evening. food is amazing g at Rasoi on MG Road.In precise you and your family would have a gala time there.Hope this helps you In planning a trip to Sikkim.