I assume you are living in the mortgaged house, as otherwise the solution would be simply to sell & divide the equity.
If your ex dies & his children get his share then they could be looked at ethically as being responsible for half the mortgage. However, legally only you would be responsible for paying it unless the mortgage lender accepted that the children's names should be added to the mortgage instead of your ex's.
You talk about the children buying you out but you still having to pay the mortgage. These statements are contradictory. If they buy you out then you receive money for your share of the house & have no further interest in it. They would have to take over the mortgage. You would have to move out unless they agreed to rent the house to you.
The alternative is that you buy out your children's interest. This would mean you raising the money, paying it to them & going on living there & paying the full mortgage.
It is important to realise that your childrens' interest in the house will not be your ex's share of the full value, but that share of the equity - i.e. the value less the amount of the mortgage.