My wife and I want to gift $25k to one child and $15k to another child. These gifts fall under the $14k per parent and neither child will have a gift tax responsibility?

[Hal_Al]

 Correct. Those gifts fall under the $14k per parent rule and none of the gifts will have a gift tax return requirement.

 "Gift Tax" is somewhat of a misnomer.  Even though a gift tax return is sometimes required, very few people ever actually pay federal gift tax. The purpose of the gift tax return is usually only to document a reduction in the allowable estate tax exemption.
See https://turbotax.intuit.com/tax-tools/tax-tips/Tax-Planning-and-Checklists/The-Gift-Tax-Made-Simple/...