These sentences involve an adjective and a participle in a row: I think that the meaning you intend is that the first adjective is valid when the participle clause is true: the omission of the when is theoretically possible but adds to the confusion. Here is the complete first sentence:
You see me happy when I am swimming
If the subject and verb are omitted form the participle clause, we assume that the subject of the participle is the same as the subject of the adjective, so this means the same:
You see me happy when swimming
If the subject is not the same as for the adjective, it is always necessary to specify the subject:
You see me happy when you are swimming
The second sentence doesn't make sene, because without a specified subject we assume me/I, and so this is what it means:
You see me happy when I am working with me.
This clearly doesn't make sense, so I think that the intended meaning requires you to specify the subject, for example:
You see me happy when you are working with me.