First temple visit planned for our one month old, forty minutes away, in this rain

My mother has planned the baby's first temple visit for Sunday. It's a small temple across town, about forty minutes by car, and the weather has turned this week with heavy evening showers. My partner is fine with the visit but wants it short. My mother wants the whole family there and lunch afterwards. I'm in the middle, as usual. Did your little ones have a first outing this early, and what made it manageable?