* However, you can not attack with your long sword and dagger in the same turn.
The two-weapon rules require both weapons to have light ownership:
When you take the attack action and you attack with a light melee weapon that you hold in one hand, you can use a bonus action to attack with a different light melee weapon that you hold in the hand. Other hand. You do not add your ability modifier to bonus attack damage, unless this modifier is negative.
So, in this version where your monk / thug holds a long sword in one hand and a dagger in the other, they have the ability to create a combination of long / disarmed swords / a tower / dagger / disarmed. They can not choose to use the long sword / dagger.
You also miss this sweet d10
Because you use a two-handed weapon, you do not wear this long sword to inflict multi-purpose damage to the d10. This is somehow a key point for the Kensei (at least until the martial arts disappear).
You can simply drop the dagger if you feel you do not need it and use the long sword completely, but you may not have it when you need it. Unless you pick it up early in the next turn. The economy of action allows it, but it is a little rudimentary and a DM can annoy it (or you could lose the dagger due to circumstances other than those related to the creature or the environment.
Sneak Attack with the dagger is allowed
As you have noted, the dagger provides everything you need for a sneak attack. When the opportunity arises, you can then choose to attack with it.
There is no flippancy
Since there is no penalty for "off-line", aside from not adding your modifier to the bonus action attack for TWF (see quote above), it is a totally viable construction option.
In 5th, the idea of left hand is a bit weird. They transferred the idea of "casual" to the bonus action attack. Functionally, you have a perfect command of both hands when using your Attack action. This is when you use the bonus action to attack with a second weapon that you lose control.
You will still need to do a hand-to-hand strike while holding your Kensei weapon to get the Agile Parry.
Just a note (in case you plan to take the Dual Wielder Feat to allow the use of non-light weapons) that you still need to hit without a weapon to activate the AC boost.