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"?

When longer wire lengths are used... the pull-ups may need to be slightly stronger to overcome the impact of copper length.  With 4.7K being the starting point, you might see improvement using 3.3K  or 2.2K instead.  Going to a lower is pull-up value is not ideal and should have you maybe re-thinking the solution... IE; maybe time to add a I2C repeater IC in the path.

The drawing software I use.  http://www.abacom-online.de/uk/html/splan.html

I guess I'm trying to figure out why you need so much voltage at the relay.  Is it a 48 volt coil?

Here is what I would have done...

Ok I spent a few moments trying reverse what you are doing...

I probably got it wrong since I only spent a few minutes... but its MUCH easier to discuss when we have a drawing.

There are chips designed for dealing with floating power supplies that can provide ISOLATION.

Example:
http://www.ti.com/lit/ds/symlink/iso7240a.pdf

[ALWAYS]

3 simple rules

Rule #1: Always ALWAYS read and honor the datasheet
Rule #2: Trust but verify someone else's design unless it comes from a manufacturers datasheet
Rule #3: Always question: "Why did some person do this in this design?" 

Regarding #1:  The best way to start understanding datasheets is to read them yourself.  The more you read them... the more they stop seeming like gibberish.

Regarding #2:   Just because you can find an example "on the internet" doesn't not make it right or "best practice". Having a circuit work "most of the time" should never be an end goal.  A good design is one that was created to work under all reasonably possible conditions.

Regarding #3:  If you are not questioning why a designer did something, you are not learning...  BUT  sometimes  hearing the "because we said so" is the easiest answer from the more experienced. 


Final note: It's always a good idea to learn HOW components work.  Here is an example of why you want capacitors across your regulated supply voltage... (including the one at your regulator)  http://www.thebox.myzen.co.uk/Tutorial/De-coupling.html

I2c is multi device communicatons bus.

No this is about Digital I/O.  We are not measuring a voltage so the ACTUAL value of the resistor is not critical.  The pin is looking for a logic change from 0 to 1 on a keypress.

The drawing is flawed.  Any keypress will be the same as ALL keys being pressed since the inputs... by means of sharing a resistor... are also all shorted together.

It's time we all started loving resistors for the very useful job they do for us.