The anti-G straining manoeuvre (AGSM) is the crucial technique for withstanding a high-G load. However if I were doing it for the kids ( as I have done) i'd make it at least double and probably more like 30 degrees. Increased heart rate (HR) is a reaction to head-to-toe gravito-inertial (G) force. Using practical sizes of timber for the A frame and concrete it starts looking feasible anything above about 10 degrees.
Doing it like this you can easily see the weight of the concrete and poles become silly big with an upright pole. Now work out the x and y components of the weight of the load and for now throw away ( place carefully on the side) the x component of both and balance up the y with at least a $2:1$ ratio. Note if you are burying the poles deep in the earth then you can also include a bit of lever action of the mud on the bottom of the pole but again this is unreliable and generally not constant. So work out the total weight of the various components and calculate the x and y components of the vector. Thus you will get extra help by the way the concrete adheree to the ground but this is difficult to calculate so should be taken as a bonus rather than a critical component. As a guide with posts in concrete the structure should be stable when you just use the weight of the components. Therefore the greatest tipping force will be when the load is parrallel to the ground. Thus you can make X any number you want and the swing wont tip it will simply start to crush the A frame. Whilst it is clear the greastest force is excerted at 45 degrees ($\frac\pi4$ radians) in simplistic terms on the Y component is the tipping force.
Also, it’s also important to note that it’s represented by the lower case g in order to differentiate it from gravitational constance G, and italics to differentiate it from the symbol of gram g. $$ A_x = -\cos\theta \left( m g \sin \theta + \frac4$ radians). Colloquially known as a force, g force is a measure which determines the acceleration produced by Earth’s gravity on an object or individual. Using a simple pendulum approximation, at the point of, the maximum tipping force occurs when the swing is at $\theta=45°$ angle.
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