Yes, kids are absolutely welcome! Solitude has many kid-friendly activities if you stay the weekend, like hiking, a kids adventure course, and biking. To get to the wedding venue from the base of Solitude Mountain, you will need to take a ski lift, which is suitable for kids 2 and older. For younger children, talk to Isabel and Adam about alternative transportation.
Solitude Mountain is at 7,900' elevation, compared to Salt Lake City which sits at about 4,226' elevation. If you're coming from out of town, you may notice you are more out of breath, but both of these are generally too low for altitude sickness.
If you're planning to stay longer in Utah, you can visit one or more of Utah's five national parks, all within a four-hour drive of Salt Lake City. Check the weather before you make your plans as some national parks are in the desert and may be hot in June. Additionally, Teton National Park in Jackson, Wyoming is one of our favorites and only a four-hour drive from SLC. Once you're there, Yellowstone is only an hour away.