You can't use car seats on the DME bus. There are no seatbelts, so nothing to attach the car seat to. If you use them on the plane (assuming you buy seats for the children -- which you'll have to do for the 2 year old and I'd highly recommend for the 14 month old), you wouldn't be checking them, so you're all set. If you aren't planning on using them on the plane and you only plan to use Disney transportation, you won't need the car seats.
With respect to your stroller, I think most people gate check them so you can use them in the airport. If you're talking a really big stroller, I think I would opt to rent one at WDW -- either from Disney or from a 3rd party. Checking a stroller is risky due to so many pieces that can be broken while being loaded, etc.