Is it worth travelling to the Yellowstone National Park in current stormy weather?

Appreciate some insight from the local folks or similar experiences. I've an upcoming planned vacation (LA to YSNP, WY) from 11-Jun to 18-Jun with 2 kids (2 and 7 yrs). The weather seems to be very harsh with ongoing snow, thunder storms and rain. I'm not sure if it is as bad at the entire park as it seems from the weather sites? The airline will charge $150 change fee per ticket. I'm trying to make an informed decision. Any advice is appreciated. Thanks.