Heya,
So there's two ways to approach it right away:
1) Stationary outdoor studio setup, where you set things up and your child has a spot to be in order for your lighting setup to be effective for what you set it up for.
2) Mobile, which requires an assistant or an on-camera flash setup, with TTL/HSS, not at all studio looking, but at least gives you fill light while your child runs around spontaneously and is not going to stay in one place.
I do both. I have outdoor setups that I prepare, measure, light, set props, etc, and then I bring the kids out. Works well for the formals that we do yearly. But when it comes to just going outside and playing, setting up lighting is pretty much a crap shoot and results in nothing because your lighting will always be off (if in manual) on a moving subject, and will never be in the right place where you want it compared to your subject, as they run around and have fun. So a stationary lighting setup, regardless of modifier size, is not going to be effective for a kid running around realistically. It's hard. They don't just play in one place of course. Outdoor, studio setup, I use my strobes (Rovelight 600) or my speedlites (YN 560 III's) in very large modifiers (up to 60"). I meter and set up everything and just bring the kid into it and do the shoot. But this requires the kid stay in the setup. It cannot follow the kid, if they run off to play or something.
Using a 26" softbox would only be helpful if the child stays in one place, faces one direction, and only good for basically filling light on the face. If the child is moving, walking, running, etc, you might as well leave this in the car.
Again using any modifier with a moving kid is going to be hard. Lighting will always be off if using manual on a moving subject.
If your child is going to be in one place, sitting or hanging out, this is all much easier and you can set up your lighting and get everything right and just shoot away. Treat it just like indoor studio. Just blend flash to ambient and you're set. Meter your flash for fill and it will blend very nicely and naturally. Gels help late in the day (CTO 1/4th is my go to for late day).
If your child is going to be moving, running, playing and you're basically chasing them with lighting, lose the stand, lose the modifier, lose manual, and go with TTL (with FEC -1 or so, just enough for fill, test it out) and HSS (if necessary, you may not need this depending on aperture & ISO unless you're in high noon bad light and full sun exposure). I use a Yongnuo 685 as my on-camera ETTL/HSS flash (because it also seamlessly goes into my 560 III fleet without needing additional transceviers) and love it, works like a charm. I set it to around -1 FEC so it's fill light when I'm outside. I use a MagGrip & MagSphere for my modifier a lot lately (got it just for this actually) because there's nothing to bounce off when outdoors. You can use bare flash with ETTL/HSS outside when you have it set for fill and it will look fine. I use a diffuser on mine because of gel inserts, and because the larger sphere diffuser makes for a larger light source than bare flash (3 times as large) so it influences catchlights, and I find it helps when I'm at close proximity to subject (where ETTL tends to over-expose no matter what) to absorb some light.
So I keep my YN685 and MagSphere (with a 1/4th CTO gel) handy on-camera when I'm playing outside with my 3 year old, since my big lighting can't chase her around. I just use ETTL/HSS with fill settings (-1 FEC at least) to help with shadows, I don't use it as key exposure. Sometime I don't need HSS at all, since it can be darker under canopy and stuff, plus I don't mind stopping down my aperture a bit on a telephoto anyways, you still get soft backgrounds, I don't feel the need to do it at F1.4 for example. I actually use my Tamron 90mm F2.8 VC macro lens the most for this, fast, has stabilization, sharp wide open, does macro, and I just add ETTL/HSS flash (the Yn685) as fill for spontaneous running around and shooting with the kid.
Very best,
:: My 
