Hello & welcome, I am Dr. B, a licensed veterinarian & I would like to help you with your wee one today.
I am very sorry to hear about Koda's situation.
If your vet is discussing removing the pericardial sac from around the heart, the first thing to know is that it is blood that is leaking into the sac due to the tumor's effects on the heart (eroding and eating away at the tissue). And as that accumulates in that small sac, it is the pressure from that fluid/blood that presses on the heart and causes the signs we are seeing.
Now if they remove that sac, Koda will leak this blood into his chest (not his abdomen). The problems that would be associated with this is that as blood pours into the chest, it can put pressure on the lungs and affect his breathing. Since the chest is bigger then the sac, this could take time before it became a problem for him. That said, the other problem with him leaking blood out of his heart and out of circulation is that this will lead to anemia (low blood volume in circulation). That can also compromise his breathing and activity because if he doesn't have adequate blood in his circulation (and he won't get it back if we are tapping the chest to remove it), then he won't be able to get oxygen to his cells as readily. So, those would be the main complications that prevent this from being a long term fix.
Overall, this tumor is a terrible one for our dogs. In this case, the surgery would buy us some time but it does have complications associated with it. Therefore, this is just a temporary fix since we cannot replace his heart with one that doesn't have this terrible tumor.
Please take care,