For a first portrait shoot I think you did pretty well! My favourite image is #3 - the two of them in front of the door... they look natural, relaxed, and it's fairly flattering for both of them
My only nitpicky comment about the shot is that I would have moved a tad bit to the left so as to centre them in the frame - it adds too much tension that he's partly cropped and she's not. You can maybe tighten the crop up in LR to equalize it, but I like the "breathing room" on her side. I love her pose and smile though, she looks totally relaxed and happy about where she is
Working with kids isn't easy, so I applaud you for getting what you did. The one of him in the tree by himself is cute, although I can tell you missed focus on the tree. I also can tell you used flash here (catchlight in his eyes) - what was the reason? When posing the family together, I find it's easier to have everyone sitting, instead of trying to lift the little one(s) up to our height while standing, especially if the "little ones" aren't so little. You can see there is some effort needed to keep him up because of the awkward look on Carson's face.
In terms of processing, on my calibrated monitor (and the uncalibrated one here at work) some of these shots are *super* yellow/orange (see #7)... Warm is good, but not this warm - definitely dial it back a bit into the cooler colour temps (#3 is the exception, this is really, really well done).
Pose-wise, this is something I'm still working on myself... I find weddings easier to pose than potrait shoots because people have things to do with their hands (i.e. bride holding a bouquet) but even then I like to take a fairly hands-off approach to posing and let them interact in front of my lens. I feel like this is what you did in #3, because neither of them look forced. Also, make sure to get her chin down (#9) - if she has to push her forehead slightly toward you to make it work, then just tell her it'll feel wierd but look great. For #6, dad's hands are too distracting, so I would have had him keep his arms down or at least find a way to hide his left hand, maybe on his son's lower back (to keep extra hands out of the shot and to keep the boy in the tree lol). Mom looks like an afterthought in this shot though, because so little of her is in the photo... I think pulling back the crop on this would help. Also, Carson does not look overly impressed to be in the tree...
When shooting next time, try to find an area of open shade with a less-distracting background. In a lot of cases, the parked cars, buildings, fences, and other objects in the background detract and distract from the photo overall. Open shade will definitely be your friend though, as it allows you to avoid dappled light, and thus the problems with dodging/burning after the fact. I avoid shooting in full sun unless there's a really good reason for it (or I have no choice).
Hope this helps, and realize most of what I'm saying is nitpicky. Great job for a first shoot, it's onward and upward from here
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