Saw it off and say no. As timun said, you might be exposing yourself to additional liabilities. End the lease without renewal, then go in and figure out what the humidity issues are and remediate before they get worse/make the tenants ill from the mold and expose you to extra liability or excessive damage to the home.
It's not your responsibility to bend the rules for them. If they need to go out and rent two homes due to the amount of people and insurance reasons, then that sucks for them, but those are the rules to adhere by. And seriously speaking, you're probably hurting more than helping by letting them stay in a home with potential mold issues and bending the rules on their behalf if your insurance doesn't cover that many people in the same dwelling.
Things might be a little different if the families were really good and quiet and model tenants, but they're not and you already have uneasy vibes about them.
At max maybe you can extend it one month to an exit date of June so that the kids finish school before moving, but I would definitely suggest insisting on May as much as possible for liability reasons and so that they can't keep pushing "oh you let us an extra month, let us longer". Also, I think the rental rates I believe would be slightly better if in May than in the summer.
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