First off, both fish are shoaling fish, meaning they live naturally in large groups. As you have the space (in a 100g tank) this is not an issue, so more fish subject to what I will say below is mandatory for the fish's well-being. Shoaling fish are stressed in groups less than 5 or 6, some need even more, and this means health issues that would otherwise not occur, and frequently increased aggression (sometimes even "peaceful" fish turn nasty solely due to the small group size). We have fish profiles here, and these species are both included. Click on the shade name to see the respective profile: Silver Dollar and Tiger Barb. Profiles in general are under the second tab from the left in the blue bar across the top.
Now to the issue with the Tigers. This species is a notorious fin nipper, and it may hound other fish to the point of death. Fish may vary from the "norm," due to many factors, but the inherent trait is still there and can be unleashed to varying degrees by again several things--including group size. If you read our profile on the Tiger, you will note it mentions a minimum of 8 in a group in a 30g tank on their own. In larger tanks, other fish are possible, with some restrictions, and the Tigers should be proportionally increased. The larger the group of Tigers the more they will be "natural" and aggression confined within the group which is normal.
Silver Dollars and any similar peaceful (sedate) fish esp with any sort of finnage should never be combined with Tigers. While some have had this work, many, many others have lost fish. I do not believe it is worth the risk of killing fish. So I recommend not mixing these two.
Even if no actual physical damage is observed, the very presence of an "aggressive" or feisty species can cause a lot of harm to other fish. Fish release chemicals, pheromones, and other fish read them. The Tigers are making it clear that they intend to rule this space, and the other fish will be under constant stress.
I would follow your last thought. Don't know how many SD's you have, but in a 100g it could be 7-8 nicely. Bear in mind they will eat live plants (most plants), so if plants are intended, this is not a fish to have. Remove the Tigers, maybe the store will exchange them for credit. Even getting a larger group now might not help; once a fish is inclined to being nippy, it is not likely to change, and the small group (5) of the Tigers may have caused this, plus the too-much-of-a-temptation SD's.