Most NYC hotels rooms are very small. NYC hotel pricing is highly variable. Are you traveling on a weekday or weekend? Many of the downtown / financial district hotels are substantially cheaper on weekends. You may be able to get two rooms.
I used to travel to NYC a lot (over 300 nights in NYC) and there are several extended stay (Residence Inn, Element etc) that may have 2 queen beds. It is possible to do NYc with kids on a budget but it requires flexibility and a lot of pre planning