I actually have a follow up question. We ski maybe only 6-10 days a season, do you think it's hard to learn/improve with this amount of skiing each year?
Note that I'm not an instructor. I'm an older skier who didn't start taking lessons regularly until after age 50. By then it was clear I would be skiing more with my daughter, as well as looking for opportunities to ski with adult friends. My husband of 30+ years is a non-skier for assorted reasons.
Based on my experience and a discussion on another ski forum a while back, skiing 7-12 days a season is enough for most adults to be able to enjoy skiing on groomed trails without thinking too hard. I think of such people as advanced beginners or low intermediates depending on how adventurous they are. It helps tremendously to take at least one lesson during each multi-day ski trip or do a multi-week lesson program for 4-6 weekends one season. My idea of an intermediate is someone who is comfortable making parallel (not a wedge) turns on most blues in the region they ski the most. Needless to say, a short blue in the mid-Atlantic is not the same as a long blue good for cruising for 10-15 minutes (with stops to enjoy the view) at a destination resort in the Rockies.
To go beyond the intermediate level and start skiing off the groomers, that's pretty hard to achieve without about 20 days, with one longer trip to a big mountain with 5+ days on snow.
While most people who live in the east or midwest choose to fly west, spending a ski vacation slopeside in the northeast while taking a few lessons can work too. Assuming someone is willing to get out on the slopes even when snow conditions or weather isn't optimal. There is a saying that goes something like "there are good conditions and conditions that are good for you." People who can ski blues in the northeast can easily adjust to skiing blues in the west. I learned that first-hand as a teen who learned in the New York Adirondacks when I was lucky to have a chance to ski a few days at Alta in Utah during spring break. Based on only two seasons, I was able to enjoy skiing green/blue groomers out west as a working adult who only did a ski trip every 2-3 years.
For a parent who learning as an adult and is also the primary organize ski trips with kids, it makes a difference if the kids are happily engage at ski school or skiing with others at times in order to allow the parent time to focus on a lesson or practice without distraction. It's a bonus if there is another adult (spouse or friend) who is a better skier willing to be a ski buddy for a few runs. Not for teaching technique, but for company on the lift and providing support in the event of a fall.
A story . . . Naomi Wain was a regular guest at Alta Lodge for about 50 years. She was a Californian who learned to ski as an adult. I was lucky to have skied a few runs with her one day after she turned 90. At some point, perhaps in her late 70s or 80s, she asked the ski school to match her up with an instructor for a Private Lesson. When the instructor met up with her for the first time, she told him point blank that she didn't need or want a lesson of any type or even a guide. His job was to follow her anywhere she wanted to ski and to be available to help in the event that she fell. I have a feeling she didn't fall often at that stage and she wanted to keep skiing in deep powder when it was available. Getting up in powder is difficult and takes a lot of energy. The instructor, JW, told the story at a celebration of her life at Alta Lodge a year after she passed away at age 93.