My guess in a case like that would be that your size 3 city has a number of units in the field that are causing the unhappiness with your republic government. Given that you have the contentment-improvements in the city, that would be the most likely cause. Other factors could be that your size 8 city is working a lot of trade or has a market and possibly a bank and thus has a fair amount of luxuries keeping people happy while your size 3 city is working non-trade squares or its trade is crippled by corruption.
The rules are applied consistently, however the situation and conditions in each city are different. You must understand the factors that go into making each city unhappy in order to apply an appropriate fix.
Within each city, look at the happiness display to determine why the city has a certain "attitiude" - click the "Happy" button within the city screen and you will see the specific factors that apply to that city's happiness (or lack thereof). It starts (on the top row) with the default happiness of that city(based on difficulty level, number of citizens, and number of other cities), then applies in order (as you go down the screen) Luxuries, happiness/contentment improvements, unhappiness due to units in the field, then direct happiness wonders. Learn how to read this screen and use the information it gives you to solve the problems.
Knowing the order these factors are applied can be important. The fact that units in the field are assessed after the happiness improvements would explain why you were seeing unhappiness despite having the colosseum (the temple is probably redundant at size 3). The colosseum probably makes your citizens content, but units in the field override that and make them unhappy again. It is because of this order that the JS Bach wonder is so valuable. Because wonders are applied AFTER units in the field, it is the only thing able to pacify citizens unhappy due to units. (Even though it is a wonder, Michaelangelo is treated as having a cathedral in the city, so it is applied during the Improvements phase instead of at the end with the Wonders.) For this reason Bach is extremely valuable for anyone wishing to engage in large scale war in republic, or especially democracy.
Edit to add: In non-representative governments, there is a line in the happy display for contentment due to Garrison units instead of unhappienss from units in the field. Whether or not you have garrison units in your city square could be part of why you see some differences in Monarchy.
