Is it permissible to donate a sum of money equivalent to the cost of a previous fertility treatment as an act of gratitude to Allah for a new pregnancy, or is it more deserving to spend this money on one's children?

You have done well by being eager to thank Allah. The people most deserving of your kindness are the closest, then the next closest. So, your husband and children have a greater right to your charity than those upon whom you bestow it. Your spending on your husband and children is charity and maintaining ties of kinship. "Charity given to a poor person is one charity, but charity given to a relative is two: charity and maintaining ties of kinship." Make this charity for your husband and children, especially if they are in need.