NY recently became the last state to enact no fault divorce. It (from what little I know — I may be mistaken) should be relatively simple to get a civil divorce by simply filing for one.
In any event, you can get a real remarriage with chuppa and kiddushin, civil marriage or not. Obviously you couldn’t file a marriage certificate for your new marriage, until you obtain a civil divorce. But that shouldn’t slow you in any way from getting remarried.
As an aside, since it is water under the bridge in your instance, one shouldn’t provide the get until a beis din sets all the terms of the divorce per halacha. If she wants to receive a get al pi halacha, she needs to follow child custody and asset seperation as halacha sets out and determined by beis din.
Hatzolcha