When is the last time you've had the farrier out? Have you inspected his legs and hooves for potential injuries/heat? The change in stride plus stumbling throws a red flag to check his feet out. He could either be in need of a trim and accommodating too-long hooves, or have an injury causing him to move differently.
Ditto for his teeth. If nothing's changed in your tack or riding style, but his head/neck carriage has changed, the teeth are suspect for uneven wear or the development of hooks or sharp edges. "Tucked Under", if it's the way I'm visualizing, face behind the vertical and breaking behind the poll, isn't good training/posture wise.
If you can get pics/video next time, it might help.
A stubborn horse walks behind you, an impatient one in front of you, but a noble companion walks beside you ~ Unknown