I have a paladin that we just leveled to 5th level. Automatically it’s making the “Always Prepared” spells that are given with the Oath of Vengeance take up the only 2 slots available at 5th level. It does not do this for the first level Oath spells though. 

I can't reproduce this bug. My vengeance paladin is showing 0 spells prepared (no additional spells are prepared).

Link the character (not share) if the bug persists.

Sorry for the ignorance on this but how do I link but not share. I see something under the words Sharable Link.

I think you're mixing things up here.

You have "spell slots" which at level 5 you will have four 1st and two 2nd level slots.

You have "prepared spells" which you can have as many as your paladin level divided by 2 (round down) + CHA mod (so for instance, 2 + 2 = 4).

The "always prepared" spells wont take away from your "prepared spells" number. If you want more 2nd level spells, then you need to unprepare some 1st level spells.

Thank you this makes a lot more sense. Actually while building a different character I started to realize the mistake (trying to replicate it). I for some reason assumed that at 5th level I just got two spells to be prepared not spell slots. My DM didn’t explain it too well. 

So stupid related question: Do Oath Spells count towards your actual Spell Slots? I think I seriously misinterpreted the RAW.

When you cast an oath spell it does indeed cost a spell slot.  What it doesn't do is count toward the number of spells you can prepare.