LDR's are also considered to be somewhat slow devices especially when returning to "dark" state.  So it's probably best to a "comparator" and averaging approach rather than reading raw values all the time.  You can create a comparator (Threshold based state change) and averaging... without very much code.

Best practice: place it close to the coil... but it just needs to be "electrically" there.  The only thing that will really change with distance is the resistance of the electrical path due to the length of the copper wire and you can pretty much ignore that variable.

The traditional diagraming with it was ugly.

Matter of opinion.  Mine is: Any diagramming with is ugly.   ...But something ugly  is better than nothing at all.

A schematic will help here...

...having us trace a pcb for you to figure out what you intended it to do is needed before any advice is given.  Maybe someone else is willing to trace your PCB.

There are some of us that have less than wonderful results with dxtreme and therefore no longer consider them an option... no matter the price.  Heck,  for me...  even free would not bring me back as a customer to dx.

The input of  standard inverter will always have the same "switch" threshold for detecting a "0" or a "1".   A Schmitt trigger has a dual threshold point for a signal that swings between 0 and 1 in a non-expected way... allowing it to be used in signal "conditioning" circuits....   EXAMPLE: You would feed an "inverter" with a known TTL compatible signal...  all will be fine.   You would feed a Schmitt trigger with a signal that did not necessarily come from a TTL family compatible device, like a LM555, a Comparator, and AC signal that has been rectified and voltage limited.... etc  and out the other side will emerge a nice TTL compatible signal with parts of it smoothed out  (state transitions reduced) where the input signal was "between" the threshold points.   If you used an inverter in the place of an Schmitt trigger there could have been a possible stream of transitions between 1 and 0 and that may be undesired.

Probably not the best explanation... now that I read it.

And if you DO decide on using the 7808 or 7805 regulators, the datasheet has the answers regarding external capacitors.  I have never seen a LM780x data sheet say that the capacitors were completely optional and only in the sample drawing to annoy the designer.   The Fairchild datasheet says, " Input Capacitor (Usually between 10uF to33uF) is required if regulator is located an appreciable distance from power Supply filter."  How far is that before I have to worry?   Not specified.  Why take chances?  The datasheet also says "The output capacitor (usually 0.1uF) improves stability and transient response."     Let's say that a 0.1uF cap is a small price to pay for a stable regulator.

When space is at a premium, you will often see 9 pin SIP resistors used  (8 resistors with one end of each resistor all tied to a common pin, with that common pin tied to GND or +5V as needed)

Spacing is 2.54mm per pin.

 

I don't know what's inside one but I imagine it's just a few diodes and MOSFETS.

Mosfets?  No, that's unlikely.

SSR's are for AC loads and though therefore have an AC component like a TRIAC (which is a bi-directional Thyristor/SCR).  It would also have an opto-coupler and some snubbing passive components along with (in the good ones) some zero-crossing based gate control.

Making your own would likely cost more than buying a ready made one... but people do it.   IE, Buy MOC3010 (or MOC3024) for opto-coupler, a ON SEMI Part # T2800DG and find some sample Triac/SSR circuits...   like...

I didn't need to make a board.  I just soldered dual row SMD headers to the tops of Machined Sockets.  The pins are bent at 90 degrees under the black plastic holder and the nicely match up with the socket holes.

That's probably just for moisture control.  If you seal up the rest in a airtight container with some dessicant pouches, you should be OK.

Now that your design is shown... its easier to say something additional.

It's not clear which precision op amp you are using... but unless you are using something like an OPA341... a single supply, rail to rail op amp... your output will not reach 5V at the analog input (OP amp output)  due to issues with the op am as well.

The output of a TTL gate only needs to be a valid LOGIC "1".   Research will show you that a Logic "1" is never guaranteed to be 5 Volts.  A logic "1" is deemed anything berween than 2.2V and 5V.   The output resistance when a 126 output is at logical "1" is determined by the output collector resistor.

You have an 85 Ohm resistor in the collector path.  If you were to look at it from a voltage divider perspective... anything lower than a 300 ohm path to ground at the output from that point would be enough to get that kind of voltage loss.  There seems to be no way you will get a full 5 volts (Same as Vcc)  from a TTL output pin in the 126.

There are very tiny smd trimpots...  but they are so small that you need special tiny screwdriver.   Using that size is called... being nice to your technician.

When asking for help... providing a drawing saves the most time in getting your situation understood.

Also, the behavior (symptom)  is common when current is being drawn from a power supply that cannot deliver the amount of current the circuit is asking for...   Unless you have really beefy relays and they are energized on power up... there is no obvious reason for high current draw unless your circuit has a very low resistance path between V+ and GND  (AKA a short)

Without a drawing... this is conjecture.  (Guess work)

And what exactly is "decoupling with a 100ohm resistor"?