There is nothing that can make your family totally safe. I have a gas water heater in the basement. Last year, a home in my town was blown to bits by a gas leak. No survivors. I have two cars in my garage, tanks full of gasoline. I have a set of shelves with propane, ethanol, toluene, you name it. Is that safe? I must think so.
In truth, we don't actually know how safe the batteries we are using are, as far as I can tell. In most cases they are being imported or drop shipped directly from China, and I don't believe they are tested to any standard recognized in Europe or the US. I I am wrong, someone correct me. I have only two types of batteries on my bikes in my garage. One is LiMn from ebikes.ca and the other is LiFePO4 from erider.com. I have talked to both of these vendors extensively on the phone and trust them and their products. That is about the best I can do. Both vendors have batteries that are 2 and 3 times what you will pay for whole batteries drop shipped from China. Is it worth it? I have no idea, but I have seen a battery fire personally and it is pretty scary to think of that in your house. In about 15 minutes, you'd be dead. I never leave the chargers plugged in at night or when I am away from home. That is probably overkill but it is peace of mind for me and easy enough to pull off.
You buy your ticket and you take your chances. I have tried to minimize risk, but I realize there is inherent risk in everything. On the other hand, people have burnt down there houses charging batteries in tools and laptops. There is no "totally safe". If the risk however is lower than the risk I take driving across town with my family for a picnic, it is in the ballpark of what is acceptable to me.
Jamis Commuter 1.0/Xtracycle Stokemonkey 36V LiFePO4, 15 ahr
Giant Boulder 9C 8x8, 48v, 10 Ahr LiMn from ebikes.ca