Personally, I'm surprised that CO offered you the hotel vouchers so far in advance. Usually hotel and meal accommodations are only provided by airport agents, and they like to think of it as a sort of last resort. If it were me, I would be pleased that CO offered the hotel (and probably you'll get meal) vouchers. Instead, in lieu of that, they will often just offer to refund your ticket price/miles, or schedule you say to fly on an earlier day/time to avoid having to put you up in a hotel. I'm no real fan of airline customer service in general (especially via phone), but in this case, I'd say you did very well by CO.

If you really want to go to PWM, in EWR, ask them to fly you to BOS, and then take DL/US/AA to PWM. If you decide to TRY this, have flight schedules available to propose times to the agents. There are flights EWR-BOS each hour. Not sure of schedules BOS-PWM. Again, whether they do this will depend on who you get at the airport. I would not recommend asking about this over the phone, because they might document your record (if they have not already) that you have been advised this would not be possible.

If you take the hotel voucher deal, they will likely put you up in the EWR Marriott, Hilton, etc. I was put up in the Marriott one night flying TPA-EWR-BOS after misconnecting in EWR due to weather. I considred myself lucky as well, because there is no rule or law that says an airline has to put you up in a hotel especially if it is due to weather. They often will do it, but again it depends on who you get.

I think the idea of spending time in NYC is a good one, especially if flight schedules permit.

I suppose there is a slim chance (say if NYC has a big weather event on your flight date) that all hotels will be sold out. Still, I'm sure they would be able to find you a room somewhere. If your concerned, check NYC weather prior to your departure. If it looks bad, then maybe have the airport representative at your departing point for EWR reserve the hotel room. Ask them to call the EWR airport CO agents, so you'll be assured of a room. Again, though, this will probably not be an issue. On the day I misconnected it was 10:00PM or later, on a bad weather day, and they still had hotel rooms right on the airport.

Perhaps your children would also enjoy doing some airplane watching at EWR?

Good luck, and be sure to write a trip report.