So before you do anything you need to run the load calculations to figure out how much of your 100 amp service is committed and actually used right now. There is a NEC formula (actually a couple optional ones) for doing this. Note that for an existing service there is some different math used to determine if you are allowed to add more to an existing service vs. what you would have to install new (when installing a new service they want you to add some overhead to it for later additions).
With that being said, I might suggest you consider installing a Wall Connector (HPWC is the old name for it). While others may jump out and say "but the UMC can do up to 32 amps so why bother", the trick is that the Wall Connector has a lot more configurable amperage settings. 13 of them to be specific. Options include 12a, 16a. 20a, 24a, 28a, 32a, etc... So you may be able to thread the needle of exactly how much capacity your 100a service has remaining. (yes I know you can crank down amperage in the car settings, but this depends on a human being remembering to do it which does not pass NEC muster - also the Tesla software has been known to reset itself back to full charge rates without folks realizing it)
Also, depending on your whole setup and deal, you might consider say running 6awg wire to it (in conduit so you can use the 75c rating of the wire) which will allow up to a 60a circuit to be used (48a of charging capacity due to continuous load derate). This would accomplish three things. 1. You get the granularity as described above, 2. You could change the setting up in the future if you removed some load from your house (convert something from electric to gas, etc...) by simply setting a rotary dial switch in the HPWC, 3. If you later decided you can't live with the slow charging rate and decide to upgrade your service, everything would be in place to make use of it once your service was upgraded. Just change the rotary dial in the Wall Connector.
For myself, I wanted to always keep the UMC in my car, so I was going to buy a second EVSE anyway, and the Wall Connector just made sense...
Anyway, just food for thought!