The phrase 'gladly willing' is correct and can be used in written English.
It is an adverb phrase that conveys eagerness or enthusiasm. For example: The teacher was gladly willing to help her struggling students.
"As a parent and grandparent, I think it's a fundamental responsibility for me and one I'm gladly willing to fulfill".
"We should be demanding more reforms than the intelligence agencies are gladly willing to offer us," said David Segal of the activist group Demand Progress.
But it should not be erecting legal barriers between honest providers of valuable services and patients gladly willing to receive them on mutually agreeable terms.
And the figures who appear in the series are its gladly willing hosts and carriers, whose personal memories represent the grand social upheavals that have marked each great era of rock's 40-year journey.
I am gladly willing to pay a few extra dollars at a Wal-Mart competitor's store in order to know the person assisting me across the counter is at least earning a decent, livable wage and has the health-care benefits he or she is entitled to.
He was magnificently intelligent -- widely read in history, all branches of science, and fluent in four languages--yet he suffered fools gladly, always willing to buy someone a drink and listen with interest to their troubles.
Sadly, there will always be people like Dan Cathy who will gladly throw their money at the charlatans who are more than willing to tell them what they want to hear.
When a beanstalk comes crashing down, Singer keeps us out on the stalk, at the edge of danger, and we gladly submit, like children willing to be fooled one more time.
The occasion will gladly be remembered as the example of a prodigious performer in action, increasingly willing to plumb music's soul.
will gladly accompany you.
Then she will gladly leave.
