Thunderbolt to HDMI (Not DisplayPort to HDMI) My first question is do Thunderbolt to HDMI adapters exist? The reason I'm specifying Thunderbolt and not DisplayPort is because I have a Belkin Thunderbolt2 Dock. If I use a MDP>HDMI adapter and the HDMI port on the unit, only one display works. However, after borrowing my friend's Elgato Thunderbolt dock and connecting it to the TB port on the Belkin dock, I could use the HDMI port on each dock on both monitors, no issue. 

I would hate to have to buy two docks to set up my docked setup, but I could if I absolutely have to. The reason I want this to work is because I have a HengeDock for my laptop, and the HDMI port is inaccessible from the dock since it points upright. 

Worst case, I guess I could get another DP to HDMI adapter, but that would occupy my other thunderbolt port, and my TB external does not have a daisy chain connector.
Mini DisplayPort and Thunderbolt are essentially the same connection, just with different hardware controlling them. Thunderbolt is essentially a combination of Mini DisplayPort and PCIe. I assume this was done for backwards compatibility with older hardware that was Mini DP (so you could use an Apple Cinema Display on a newer model MacBook Pro, for example). Of course, Mini DP doesn't have the same power behind it (in that it doesn't combine with PCIe) as Thunderbolt so you can't daisy chain them.

Unfortunately, from what I have been able to see, and from my product knowledge working at an iStore, there is no Thunderbolt to HDMI, only Mini DP. The actual daisy chaining that goes on inside Thunderbolt devices is done within the device itself and would require a power source to power it. Since there is no power source to an adaptor, there is no point making a Thunderbolt to HDMI connector when Mini DP is (for all intents and purposes) the same thing. Apple also says here that if you have a Thunderbolt chain, the Mini DP connection should come last. This could be the reason for only one of your HDMI ports working as the built in one would most likely be positioned after the Mini DP connection.

Of course, that isn't to say there is no multi-output HDMI Thunderbolt peripheral (a single Thunderbolt cable to a device with multiple HDMI ports), it may exist as it is possible, I just haven't seen one. The closest I could find for you were these two devices, Mini DisplayPort to HDMI® (2x HDMI® Output) Converter w/ Audio and Zotac ZT-MDP2HD Mini DP to Dual HDMI Cable.