If you are thinking about doing the lap infant thing, make sure to consider the cost of that in your award comparisons. Aeroplan has the most generous policy that I know of - $50 or 5k miles for lap infant in economy, double for business. Not sure if that's round trip or one way, but a great deal either way. If you can find award seats where the over water flight is on United, Turkish, Swiss, SAS, Brussels, or EgyptAir metal, you will avoid fuel surcharges when using Aeroplan miles. Aeroplan does charge 37.5K for economy seats to LCA, so another point to consider. Their business rate is good though - 52.5K.
Also consider using BA Avios to get to NYC. Search for awards to LCA from NYC - you'll have much better availability. From CLT in Star Alliance we only have CLT-MUC on LH and otherwise are reliant on spotty United saver seats to EWR or ORD. On the other hand, it's usually pretty easy to find saver seats on US from CLT to one of the NYC airports. You could do the same for ORD but with your family in NYC it makes more sense. Of course you'll need a safe layover buffer if you book separate awards and don't stay overnight in NYC.
I would try to avoid oneworld. Even though you're in a OW hub, it looks like only BA flies to LCA of the OW European carriers. That means you have to transit London, and most likely LHR. Plus the fuel surcharges on LON-LCA. Better to avoid altogether if you can. I saw CLT-LHR-LCA on US metal for the transatlantic flight, and the total chargers were almost $200 per person, one way.