Keep the heart rate slow, give them milrinone if you absolutely have to, and avoid AF like the plague.
The limitation of right heart preload by a stenotic tricuspid valve manifests as right heart failure. Hepatomegaly and portal venous congestion with ascites tend to complicate the picture.
Mild tricuspid stenosis is usually well tolerated. Your normal valve has an area of 7-9cm2 and major problems don't tend to begin until after it decreases to about 1.5cm2. At that stage, exercise tolerance becomes limited.
Interestingly, this is a very low-pressure system; the normal gradient across this valve is only 1mmHg.
Moderate stenosis is considered to be a gradient of 3mmHg.
Severe tricuspid stenosis is characterised by a valve area less than 1.0cm2, and a gradient of 5mmHg across the valve. Significant right heart failure (well, really biventricular failure) tends to occur.
Atrial fibrillation is even more disastrous than in mitral stenosis, particularly in underfilled patients, or those who have recently had their ascites tapped.
Preload needs to be kept high. The pressure driving the blood across this stenotic valve is really your CVP, and so one needs to keep the CVP abnormally high in order to maintain normal RV diastolic filling. Venodilators such as GTN are to be avoided.
The heart rate needs to be kept slow. The RV needs time to fill in diastole, and without sufficient time to fill the RV all chambers suffer decreased preload and thus decreased stroke volume. Ideally, it should be 50-70. Of course, too low and you will see the effects of decreased heart rate with a fixed stroke volume, so this is also to be avoided.
Survival of these patients depends on the maintenance of sinus rhythm. Atrial fibrillation tends to be followed by a complete cardiovascular collapse, as empty ventricles struggle to produce an adequate output; the sympathetic compensation to this tends to increase heart rate and impair RV diastolic filling, driving the cardiac output lower and lower in an accelerating spiral towards cardiac arrest.
Contractility of the right ventricle is fairly important. With a fixed stroke volume, forward flow of blood through the pulmonary circulation depends on a forceful ejection. Loss of RV contractility (eg. due to beta blockade) tends to decrease cardiac output and is therefore to be avoided. On the other hand, you want to avoid tachycardia as best you can, so dobutamine may not be a good choice. Milrinone may be of some use.
Systemic (LV) afterload is somewhat meaningless in tricuspid stenosis. However, it is fairly important to maintain a reasonable smooth muscle tone in order for the central venous pressure to remain reasonably high. Thus, if the patient develops systolic hypertension, it would be better to treat this with drugs which act on the arterial circulation, such as calcium channel blockers.
Similarly, pulmonary arterial pressure will not have much effect on RV function. High or low, it doesn't matter- the RV systolic performance is limited by the low flow of tricuspid stenosis, and this will not be altered by decreasing the pulmonary vascular resistance.