Yes, a voltmeter comes with two probes . . . and you can get the cheapest of the cheap, analog voltmeter to perform this check.
It's very unlikely that you have any isolated grounds if you didn't specifically ask for them. Also, all of the grounds MUST be connected together at the breaker panel to meet code . . . so the grounding at the breaker box is fine.
As far as the "two physically separate boxes", I was referring to the electrical boxes that have the outlets in them, in your listening room . . . that is, does each circuit have its own box & wall plate, or do they share the same? If they share the same box & wall plate, then all the electrician needs to do is to make sure that all of the ground wires, from both circuits and all outlets, are physically connected together here (in your listening room).
If they're completely separate boxes, plugs, and wall plates in your listening room, then there's not a whole lot you can do without being very questionable in terms of electrical codes. If this is the case, then simply using one of the circuits is better, with a high-quality power strip or conditioner. Or if you have any components which have a two-prong plug, you can power them from the other dedicated line, and have no grounding issues.