Good stuff on the additions. Need back work too, like deadlifts or rowing, then you will be balanced. Consider that back issues are incredibly common, missing this is not advised.
Everything counts, there are no exceptions. I remember posting to one person feeling the need to get fit to be a better dad that you will never be fit enough to keep up with a child, they will simply expect more, and still wear you out. If you can't do the fun stuff there really is no point anyway!
I know you are used to P&F being the LO distraction, great show, I love it, but there is an alternative. You can be the distraction.
My son hasn't been 3 in a while but my wife and I used to provide him endless entertainment when training at home before this age. We have his tooth marks on some little handbells, pink for our shame, that came in a kit we bought to help with my wife recovering from an operation, so he really has cut his teeth in the gym. That colour was on offer, my wife is not what one would call a pink person.
The at home kit is a lot more serious now but back then only low intensity stuff was done at home. Entertainment was him copying to some extent, either simply moving his arms and legs about when he was too young to stand, smiling and laughing at our funny faces, then doing some of the movements with no load while laughing at us for being so slow, i.e. doing the exercise properly. By making it a bit of a game, it meant he wanted us to be doing training, as it became family fun time. His form was dreadful and erratic at best but safe, it didn’t matter back then it got him moving.
As he got older we recruited him as a coaching assistant, basically telling him to watch out for specific failings on movement and tell us if we did it, he's still doing it. Being home educated PE is often him and my wife doing circuits, we have him watching for my wife's form to help enforce how it should be done in his mind, lot more strict with him now he's not a toddler. Obviously the intensity is child standard low, unlike with mine, but he will sit there being powerlifting judge and is very good at it. He doesn't care how much I am lifting, the bar is more than he is allowed to even consider at his age, so it's all heavy. All he sees is movement so squats are right depth, smooth movement with no stalling, no forward dip, knees following feet, or dad gets told off. It takes a bit for an aggressive trainer like me to take criticism from a child with good grace, but I keep in mind that I have asked for it and he knows my voice sounding sharp after a set is nothing to worry about.
If you ever read my jounal, it may be worth considering that on all the squat sessions my coaching assistant is someone who is still losing milk teeth
Adding to Goldie's comment
Bench pressing and squatting the LO is not a bad plan they love being on shoulders and lifted about. I used to do a form of good mornings with my son, have him on shoulders knees slightly bent and lean forward until he was nearly able to touch the floor, the most difficult was having a weight that was shaking as he laughed like a loon, because of course what I was doing was so sensible.
