I've done two trips with kids. Slovenia and Switzerland/Italy (accessible from the same lifts).
Slovenia was a steal and it was great. Skied at Vogel in Triglav National Park. Stayed in Bled which is a great little town. AirBnB was cheap, weekly lift tickets were like 150 euro for adults and kids were half that, food/drink/entertainment was reasonable. It's not a huge mountain by any means but it was enough and the snow and conditions were great. We do a bit of backcountry skiing as well so that broke it up a bit. Even with airfare, we were ahead of a Vail trip.
Switzerland/Italy I'll give you probably isn't cheaper overall but it was pretty close. Skied Matterhorn Paradise and stayed in Zermatt. Best part about it was one of the main lifts basically takes you to the border ridge of Switzerland and Italy. Skiers choice which country you want to go down into! AirBnB in Zermatt, resort town prices on everything there. The pictures from that trip are worth the nominal extra we paid to take it.
My general advice is to look up the countries or areas you want to go and see if they offer multiday/multi resort passes. Because there are probably going to be a lot of them and they're likely pretty cheap. That's where the difference is made up in the airfare.