It’s phrased oddly. It should be more like “My dream ticket for the Democratic party, the side that has the experience,…”. It’s saying their dream candidates for President and Vice President are Bill and Hillary Clinton.

It is possible to quibble with the grammar, but I say it is basically OK. Although the sentence lacks a verb, the hyphen is easily interpreted by a listener as a placeholder for the verb: "is". Stripped of all its subordinate clauses, the sentence is: "My dream ticket (is) Hill and Bill." My only real qualm with the sentence is that since there are two people on the ticket, the sentence should be corrected with: "who have the experience, who are respected..." It would be acceptable to leave "has" and "is". However, if you do that you need to replace every "who" with "that" since you would be talking about a thing (the ticket) rather than people: "my dream ticket that has the experience, that is respected, that can get the vote"

You miscopied the original. … who has experience.. (good) … who has experienced.. (wrong) You could say ‘who’s experienced’ though.