I have rain pants and a jacket and my two kids sit in a tent on the back. They love it. I love it. Together we have put over 2000 miles on the bike in two years.

Patagonia makes great rain jackets that have hoods that can adjust to fit over a helmet.

https://www.ternbicycles.com/us/accessories/473/storm-shield

What about safety? I have an ebike too similar to yours, I bring both my kids (it requires some serious efforts on steep hills with both kids though), but I fell down once in the rain that gave me a decent scare, especially since my wrist is taking so long to recover and I could have hurt my daughter (lucky, nothing happened)

I took a spill with my kids over a bridge that had black ice. Luckily everyone was ok.

We all wear helmets, we almost exclusively use bike/walk infrastructure, and we take it slow.

The biggest risk in my mind is interacting in any way with cars. And so I avoid cars on our routes as much as possible. And I regularly “break the law” by riding on sidewalks because paint on the road is not bike infrastructure and my life is more valuable to me than some ticket for a ridiculous law.