I have two small rooms (about 15 feet apart) - one 8 by 10 (8 ft ceiling) and the other 11 by 15 with an 8 ft ceiling that I want to cool with a mini-split system. Both are reasonable well insulated (R 14+ or more). The smaller room is for a small hot tub, the larger is for my shop office in which I plan to home brew beer and wine. So 80 sq.ft. and 165 sq. ft. respectively. I can not consider how even a 9000 BTU exterior unit would be overloaded by two inside units. I have a automotive hvac license - will take the household if I need to. I ask your opinions please on adding a second interior unit to cool both rooms!
Multi-zone outdoor units are a thing...
There is such a thing as a multi-zone mini-split heat-pump system -- most of the major mini-split makers make them, with options ranging from 2 to 4 or even 8 zones.
however, they may not come in a small enough size, so you may be better off with two separate systems for the separate buildings
The downside is that the smallest multi-split outdoor units are generally in the 1.5ton (aka 18kBTU) range, with the matching indoor units going down to 0.5ton (aka 6kBTU), and the need to have no capacity "left over" in the system that's not able to be used by an indoor unit somewhere as a design constraint.
This, along with the distances involved, mean that you may be better off with two small through-the-wall or packaged terminal heat pumps (6-7kBTU each -- Amana has some 7kBTU, 230V units for instance) instead of trying to make a single multi-split do all the work for both buildings.