The short answer is "yes, they *could* be awarded." However, an award against you based strictly on the facts posed appears unlikely.
As stated by other attorneys on this forum, awards of attorney fees are generally the exception rather than the rule. Judges tend to use them to address behavior that is unusually unreasonable, costs the court or parties additional money, or that is frivolous/bad faith. The other circumstance judges tend to award attorney fees is where it would be equitable to do so. (i.e. neurosurgeon husband ordered to pay for fees for unemployed wife who was forced to hire attorney by borrowing from family).
I generally tell clients that, so long as they act in good faith and take reasonable positions under the law, the chances of being hit with attorney fees tends to be quite low. Sometimes, as it sounds in your case, a lawyer will use the threat to bully an unrepresented party into accepting an offer. In addition to being poor legal form, it also tends to broadcast a weak position (why make threats if you have the law on your side?).
Incidentally, if your spouse is taking an unreasonable position with regards to moving a child out of state, s/he may actually be putting him/herself at risk of being hit with attorney fees. Also beware that if you intend to seek attorney fees at the conclusion of the case, you *must* file something prior to trial that indicates that you intend to do so. Presumably your lawyer has done this already. Best of luck!