@stacyih, as a previous resident of New Orleans (in the last century) and a current instructor at the Canyons I just had to comment. There's a lot of good advise in the above.
One item is 'slow down', not just in rental but for everything the first couple of days. You are coming from sea level and the base at Canyons is about 6800 feet. It takes time to acclimate. The beginner area is at the top of the Red Pine gondola at about 8000 ft. As has been said, drink plenty of water. The Red Pine Lodge is right next to the teaching area so taking breaks is easy.
Rental, if you are renting from Canyon Mountian Sports get there early, early. As noted, if you can do it the evening before so much the better. At that time of the season you want to be at rental an hour before your lesson time. I'm not sure what time they open during the holiday season bet I don't think it's earlier than 8 AM. You want to be at lesson check in, between the gondola and Orange Bubble by 8:45. That will be tough to do with a huge line in rental. It's not unheard of for beginner groups to go up at 10 AM due to long lines in rental.
First lesson. I'm a proponent of Mom and Dad being in one lesson and the kids in a different lesson. At Canyons you will start on Sweet Pea, a very gentle slope with a surface lift to the right of the top on the gondola. You may spend your entire first morning on this slope. You would then progress to the High Meadow lift in the afternoon. This is right in front of the Red Pine Lodge so getting around is easy. Mellow Moose is the training run off of High Meadow. It's a good training area with many different pitches so progressing to steeper pitches is easy; it's all rated Green, so considered easy. Once your instructor is comfortable with your turning and stoping ability you will progress to Snow Dancer off the Saddleback Chair. This chair is again in front of the Red Pine Lodge. This is a natural progression from Mellow Moose and not uncommon for new skiers to be on this run on their second day.
At this point you have options. The Park City base has more Green runs than the Canyons side. It's a short bus ride (free) from the Canyons base to the Park City Base and the bus drops you off right at the enterance to the lifts. There's no problem transferring a lesson from Canyons to PC you just need to let the ski school know the day before.
Transportation. In addition to the free bus there is also Canyons Village Connect,
https://cvma.com/canyons-village-connect/. This is s free shuttle service for people staying at Canyons Village. It's sort of like a free Uber.
Lesson perk. If you can swing it another benefit of skiing with an instructor is using the Ski School lift line. It's usually shorter than the regular line. Also as previously mentioned an instructor will guide you to the better ways down. On the PC side Miners Camp is a great place for lunch. It's accessable from Greens and after lunch you can ski back to the base on Homerun off the top of the top of the Silverlode Express. Don't be surprised if this takes you the rest of the afternoon to get down even though it's a Green run, it's that long. Or at least you'll be ready to call it a day. That would be a lot of skiing for your second or third day.
Expectations. Don't be surprised if you can't keep up with the kids after three days. The kids sound athletic so they may pick it up quickly. However, if one of them is very cautious they may want to go slow. This can make it difficult to ski as a group. Take your time don't get frustrated if one child doesn't want to go fast. Ski short segments and regroup but let everyone ski at their own pace. Skiing can be a life long family sport. I haven't been able to keep up with my kids for 20 years but we still enjoy going out with each other and then talk about it at the end of the day.
Welcome to the wonderful world of alpine skiing, enjoy.
Should you have some specific question PM me I'll do my best to answer it.