Boy, this is an impossible set of questions to answer without knowing a whole lot more information. Let's start with the easy part:

"Can/should individual breakers be changed?"

Although this may seem the easiest approach, it is potentially the most dangerous. NO! Don't just put in bigger breakers without understanding all of the specifications of the wiring.

The primary purpose of circuit breakers isn't to facilitate the number of appliances you have; breakers are designed to protect the wiring and fixtures from becoming overloaded and starting a fire.

The "first principle" here is that breakers need to be matched to smallest wire guage on the circuit. Thus, a 15-amp breaker is typically used to protect 14-guage wire, a 20-amp breaker protects 12-guage wire and so forth. If you swap in a 20-amp breaker on a circuit designed for 15 amps (e.g., #14 wire), you're creating a fire danger.

[There's a bit more to it than this, but that's a good starting point.]

"The builder...installed a wine chiller beneath the counter but no other appliances.

Assuming the builder knew the counter was to be used as a kitchenette, s/he should have installed two (2!) 20-amp circuits serving only the countertop. (BTW, each of these circuits should have its own breaker.) If that's not the case, there is no way of making this a servicable, code-compliant kitchenette without running one or more additional circuits.

In short, this has much to do with the circuit wiring than the size and/or configuration of the breakers.

"How can we make sure that the wiring can support the demand? The subpanel that serves that space is no where near full."

It doesn't matter how many unused slots there are in the subpanel--that tells us nothing about the amount of available power or the existing load demand. Nada!

If you can post an "accounting" of the following, the members here may be able to provide some useful advice:

1. In the main house panel, what is the rated size (in amps) of the circuit breaker that feeds the guest suite (including other parts of the garage, too). Bonus question: What size (guage) is the feeder wire from the main panel to the subpanel?

2. What circuits are already present in the subpanel? (Example: 20-amp for garage receptacles, 20-amp for wine chiller, 15-amp for guest suite lighting...and so forth.) Please include ALL the existing breakers.

There may be more information needed, but that's a starting point.

First, thanks for preventing a possible house fire. Seriously.

As far as I can tell, there's just one 20 amp circuit for the counter top (one breaker, two outlets, if I'm following it correctly.) Also, dh told me that I was looking at the wrong subpanel before, and the one for that area is full. It will take a little time to get back with the answers to your questions about main & sub panels. I appreciate you taking the time to respond.