Those three kids are pretty lucky to have you taking them on such a great trip!
If you are looking for a guided pheasant hunt at a lodge, we have a couple of options for you in South Dakota. They offer the great hunting SD is famous for. Let me know if you would like more details.
There is plenty of public land to hunt across the state of south dakota, a little investgation and some maps would be a good start also its not terribly difficult or exspensive , sometimes free if you ask the right people to hunting access.
Most of the pheasant hunting is getting way overpriced for a couple of birds. Most outfitters in SD will run in the 200-300 per gun per day and some will include lodging for that but most wont. From my experience most of the outfitters provide dogs and guides if you want them.
How old are the kids going?
Do you have your own dog?
Can you tolerate a little cold weather?
My best advice if the kids are up to hunting when it is a little colder is to come up and hunt in december. There are less people hunting now and if you find the right landowner they may let you on for nothing later in the season. A big, big help is if you can come up mid week also. No one will be hunting and landowners and their families usually hunt the weekends. If you want ideas on where to go I have several nice spots of public ground that have worked for me in the past, just let me know (firstname.lastname@example.org). Also, if you have a kid that is more assertive use him/her to ask for permission. This may help some and gives them the experience of talking to landowners which can be invaluable. Hope this helps.
As a Taxidermist I look at hundreds of Whitetail Bucks every year. I know that I have seen many different ways people judge the size of racks on live deer. I think for the most part they all are pretty close. I'm going to give you some measurements that I have noticed being right on in just about every deer. We have used it in the last couple years and have only been off by about 5-6 inches. We do study the deer while bowhunting so we get a little more time to look at them....