Honestly, that’s not known. maybe yes, they can remove a Kage from their post, however, it might not be a decision that the shinobi will accept. They operate as a separate entity in some regard.
In the past, the shinobi have come to subjugate themselves before the Feudal Lord. In return, the Feudal Lord gave the shinobi funds to create and mantain their Hidden Village and serve as his national military. However, since then the shinobi villages have become so self-efficient that they can maintain themselves through missions and actually produce more GDP then the entire country combined, so they actually make the nation money instead of costing it money. In theory, at least economically and militarily, this means the Kage has much more power than the Feudal Lord.
My theory is that the Kage and the villages mere follow the Feudal Lord out of a sense of respect and duty. For if it weren’t for the Feudal Lord, their village never would have happened. You could consider the Kage a “Chief Executive” while the Feudal Lord is the “Head of State”, as with most Heads of State, they serve more of a ceremonial role in the system than anything else. However, the Feudal Lord can affect the village’s income, as seen with the Feudal Lord of the Land of Wind outsourcing missions for Suna to Konoha instead. However, it should be noted that this Feudal Lord “was replaced” sometime between Part I and Part II, possibly haven been removed from power by force. I would imagine as long as the Feudal Lord doesn’t contradict the best interests of the village, the shinobi of the village as just as loyal to him as they are the Kage.