What is the Dowager Countess of Grantham's source of money?

There's no evidence that I can find that Violet Crawley has any income other than from the Downton Abbey estate presumably by way of a stipend from Robert.

Indeed the wikia says...

While she was born into the aristocracy, her family was relatively impoverished and she brought almost no money with her upon marriage. When she married the Earl of Grantham sometime before 1860, she brought her upper class blood but little money into her marriage.

It's possible that she may have money saved or invested from previous stipend payments but given the culture of the time it's unlikely that Violet would talk about money unless she had to.

The Downtown Abbey estate is entailed which means that...

Unfortunately, the Earl does not own the estate outright. It is entailed. An entail was a legal device to ensure that property would be handed down in a way that suited the ancestor, normally to a male heir, thus keeping the family estate intact.

In the entail system, the property owner, The Earl’s father, does not pass it in fee simple to the son. The Earl has a life estate, meaning he has the full use of the property during his life and, at the end of his life, it will pass to his son or to someone else in the family- often the closest male heir.

^Source

Death duties / taxes of the time were vicious to the landed gentry and tying up the money in trusts and other legal procedures would have been the norm.

This may be what Martha Levison is referring to as "tying the money up tight".