Legal Question in Wills and Trusts in Pennsylvania

I do not have enough information. You say your father had no will. Then how do you know that your father set up an investment? Do you have proof of say, a 529 college plan or something? If you only have his verbal assurance, then you have nothing.

Is she allowed to cash in this investment? It depends on the investment type and what it allows.

If your father really set up an investment, he should have created a trust, either in his will or a revocable living trust. If he had done so, then the answer would be for you to review the trust. The trustee (assuming it was your father's wife) could only manage the money for the benefit of your children. He could also have some sort of designation paying the funds to your children, but the funds should have been paid to their guardian long ago if he had done this, so my guess is that he did not do so.

In answer to your question, no, your children are not responsible for paying your debts. But this assumes that the money was theirs to begin with. I don't know if in fact it was. If the money was given to the father's wife via this alleged "investment" then its hers, not your children's. And if she retained ownership rights in the 529 plan, it might be possible for her to liquidate the funds. There might be tax consequences and I would have to know the specifics of the plan (if there was a 529 plan) to be able to tell whether your father's wife could do this.