I agree, it's not about rights as such, it's about what is best for the DCs. He may say he has a right to 50/50 or you may think that as he left, his right is only to see them when it suits you. Neither those may he in the best interests of the DCs.
Financially, every situation is different and you either come to an agreement after months of arguing or you spend thousands letting someone else decide for you.
Either way, as painful as it is, the easiest and cheapest way to resolve any issues will be between yourselves. Keep things on topic, keep it civil, if necessary involve a 3rd party to stop it descending into a bunfight if you're face to face. But essentially you have to sort it out so that the DCs are as happy as they can be with the situation.
So sorry you're going through this, but many people come out the other end stronger, more independent and with some free time to enjoy with friends and new partners. It doesn't have to mean the end, it's a new beginning. 