You just never know how the hormones will strike the gander - especially if the kids play close to where the geese are fed / and lay their eggs. If you get another goose now, they will have time to get to know each other, and the kids before the breeding season hits. I have American Buffs and I have had no trouble this year, but last year I had an extremely protective gander that I had to rehome to a non kid household. He was fine during the rest of the year, but he considered an amazingly large area as his mates, and would attack you even through the fence 100 ft away during the breeding season. He was an exception though - this year, all my geese were extremely laid back and tolerant as long as I wasn't actually trying to count the eggs in the nest.
That gander knocked down my 4 year old - he was fine, however, it did shake him up a bit. I was right out there with them but looking in a different direction, so I didn't catch the ganders rush. If he'd been out by himself the goose could have repeatedly knocked him down and it would have been hard for him to get away. Plus, he would have been traumatized and be afraid of the geese. HE had gotten too close to the nest. Young children should not be left to play unsupervised near breeding geese - I have mine leave them strictly alone during the breeding season. -- older children probably will be able to deal with them just fine.
One possibility is to put up some kind of moveable temporary barrier between the main goose area and the kids play area, at least for the first few weeks. The ganders are worse once the goose is sitting on her eggs full time, so you could always pick up the eggs to prevent that. It wouldn't need to be expensive - even the plastic bird netting would work. It would help young kids to give the geese a wide space. Sometimes the geese also get aggressive with the other birds - mine mainly left the ducks and chickens alone, but you never know.
I would also recommend teaching the kids if they are old enough how to deal with geese. Geese do like to be in charge, and you don't want them thinking they can push people around. However, a younger child may not be tall enough to properly deal with the geese --- they listen now to my 10 year old much better than they did when he was 7. Standing tall, do not run, waving arms / sticks to make yourself look bigger etc.
Right now, I have one goose on eggs with a laid back gander -- He only gets upset if I go up to her nest and make her upset . . . the rest of the time he wanders around the field looking lonely. I'm sure your bird would love some company! I hope that you can figure out a way to get him another goose or two . . .