I can see that the bees really worry you. I’m wondering why? They’re bees. Bees are tiny, eat flowers and live in your neighbours garden. I know they sting, but they aren’t the dangerous, slavering beasts you seem to be making them out to be.
I don’t know how this woman’s husband got stung by dozens of bees, but unless her husband was standing right next to their hive and ranting, I think that’s very unlikely. My mother kept bees, and when we lived in her house, my friend looked after them and they never bothered us. We had birthday parties within metres of their hive, my child played normally, she climbed in the apple tree and bust swings and treehouses (bees love apple blossom) we had a paddling pool. She was never stung. I was once, when offering my friend a cup of tea as she was opening the hives, (i often watched, was only stung the once) I’ve never seen a swarm, it must be fascinating (if slightly inconvenient for a day or two)
There’s no reason to assume you child will be ‘terrified’ of the bees unless you teach them to be terrified of them (which you seem to be). They are just insects, and very beneficial ones at that. You have the opportunity to choose to teach them to be fascinated by these hardworking and essential little creatures.
Might I suggest you learn a little about bees before you decide what to do? They need to drink, but cannot land on water, so need stones or something next to it. A paddling pool will just kill them. Provide a dish full of pebbles and water and they will drink from that. Swarms are their way of multiplying and finding new territory. They may assemble or rest near the hive, if the weather is mixed and they can’t fly off right away, but they won’t settle, because they want to find a new patch. Swarming bees rarely sting, as they are loaded down with honey for the journey. A beekeeper will come and collect them for you (they are quite valuable) and you know where your local one is, don’t you? If they’re all in the a tree, they won’t be bothering you on the ground, will they? Bees are aggressive. They die if the sting you. They will die to defend their hive but if you leave them alone, they’ll leave you alone, unlike wasps which are aggressive, vindictive little sods.
I think really the issue is with the you and the neighbour, not the bees. I’d be delighted. Loads of people keep bees gardens. It’s not a big deal.