I am so sorry for your pain and loss. It is a loss, if only of time. I know how you treasure all the little moments you have with the kids.
I have to say that if your ex is doing the asking it puts a different light on the whole thing. I agree that it really puts the kids on the spot and I don't know that she isn't using guilt. I would hope not, but...
If you can stay out of the courts, that's probably best, have you talked to your ex about how often the kids will come home? Does she feel it her "turn" to have them? Has she said anything about all of this to you esp acknowledging how difficult it must be? Is she open to negotiation?
My D's are right in the same age range as your kids and like you, I feel I'll be loosing them way to soon as it is. I don't have any wise words for you. It sux and it isn't fair.
Do talk to the kids about how you feel. They are your children and therefore I trust the can be compassionate and understand that you aren't trying to guilt them into anything.