I think it suited Sauron's purposes to have the Balrog in Moria, at least until he started moving his armies into the attack. It helped make the Misty Mountains a formidable barrier, and he was aware that the Ring was in the Shire and, subsequently, in Rivendell. So there was no reason for Sauron to try to give orders to the Balrog at that stage.
Had the Balrog survived the Fellowship's passage through Moria, Sauron may well have tried to enlist him into assisting in the assault on Lothlorien, or possibly an attack on Rivendell. Whether he would have succeeded in persuading the Balrog to his cause is another matter. Quite possibly, he could have offered sufficient inducement for the Balrog to throw his lot in with him, but the Balrog may equally as well have refused, preferring to stay safely tucked up in Moria.
Either way, the Balrog would have had free will: whether to assist Sauron or not. It is not a foregone conclusion that he would have done. And if the Balrog had refused, there was not much that Sauron could have done about it. It's unlikely that he would have wanted to waste resources trying to teach the Balrog a lesson.
[ March 12, 2003: Message edited by: The Saucepan Man ]
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