You're not missing anything; it's OK as it is. Heed the advice of @Paul_B on wiring though.
The 'problem' is that you keep mentioning in your schematic a 'led driver'. A led driver as such is NOT a 12V power supply. However...in this case, it probably is. I know this is confusing, but the confusion mostly boils down to the inappropriate/inaccurate use of terminology by producers and sellers of (low cost) electronics.
A 'led driver' does exactly what the label says: it drives leds. Leds need to be fed with constant current and as such, a led driver is generally a constant current source (ccs). This means that regardless of the voltage it needs to put out (within reasonable limits), it will always try to supply a certain number of amperes/milliamperes to the load. Led drivers also generally have a dimming input for either an analog or a digital (PWM) dimming signal to reduce the light output of the leds.
Due to its task, i.e. supplying constant current, a led driver inherently does not have a constant voltage output. In other words: if you have a module that requires a specific voltage (12V), a led driver is not a good choice, since it may give a higher or lower voltage as a function of the current that is actually drawn by the module.
A constant voltage power supply is what you need, and that does exactly the opposite of the led driver: it tries to keep the voltage constant, no matter how much (or little) current is consumed by the load. Of course, again within reasonable bounds. This is what you need for modules like relay boards etc. that need to be fed a specific and constant voltage.
Now, why is the above relevant to know, but not necessarily a problem with your component choice? The issue is that these days, many sellers (especially on eBay, AliExpress etc.) sell constant voltage supplies intended to power led modules, and call them 'led drivers'. This is not accurate, and actually confusing, as they technically are NOT led drivers! This happens because many led modules (such as the popular led strips that you can cut to any desired length) have the current limiting electronics built into them and therefore want to be fed with a constant voltage.
It seems that you have one of these so-called 'led drivers' that is in fact a constant voltage power supply, more specifically a small switch-mode power supply. If so, it will likely work fine as a 110VAC to 12VDC converter.
However, it makes more sense (also economically) to just search for a '12V switching power supply' and then pick a unit that can supply at least the amount of current your project is expected to draw at its peak with a margin. Generally, by searching this way, you'll find more, cheaper and potentially also smaller power supplies that actually do what you want.
Give it a try; I'm sure you'll quickly find unboxed SMPS modules that are even smaller than the one you have now, or the Meanwell-style power supply units that come in shiny metal boxes with screw-mount terminals on one side. They generally work quite well and are very cost-effective.