You say in your post "the right front wheel drops down while the left front stays in place." so that should tell you there is something wrong with the right side, take off the right wheel and move the shaft and see if there is play in it before the left side wheel moves up or down.
Thanks for your patience with me. Maybe some photos will be helpful:
Axle in the up position as seen from under deck
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Axle "dropped down" as seen from under deck
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Axle "dropped down" as seen from outside deck
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Closeup of axle "dropped down" as seen from outside deck
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I hope this might clarify what I have been trying to explain