There is no direct way to center a trace between two pads other than manually specifying coordinates. That would be a bit silly. However, there are ways to address your issues.
Actually, ease of solder has nothing to do with how close other copper is, as long as that other copper is covered by solder mask.
Avoiding shorts due to too close traces is handled by defining minimum clearance distances. The absolute minimum is what your board house can reliably do, and that should come from them. Unless you are doing something unusual, use 8 mil minimum clearance. Any board house around the world can do that reliably nowadays.
Additional clearance beyond the board house design rules may be required due to the voltage between traces. 8 mil is fine up to 50 V or so. If your voltage is higher between some nets, then you should create net classes for them and specify a suitably large clearance between those net classes. Do HELP CLASS for details.
Otherwise, don't worry about whether a trace is exactly in the middle between two pads. Specify the rules, and Eagle will follow them. Going between two pads isn't a special case, and you shouldn't try to make it one.