I would first ask myself, why is the client picking typefaces at all? Are there brand standards in place I have not been made aware of?
For the record, there's nothing which states two or three or fifteen typefaces are too many for a logo. If designed well the quantity of typeface variation is irrelevant. If you can pull off a great logotype with six fonts I doubt anyone will "ding" you for using too many typefaces. Simple is generally better, but ultimately it's the final imagery which is of primary importance.
Often I find clients micro-manage in this way because A) they want to feel included in the processes. Which is actually great. and B) the client isn't being directed in a proper manner.
You need to treat the clients correctly and while giving them choices, give them directed choices. If your client is aware of "dafont" then you've got a battle on your hands. You need to provide solid conceptual designs and direct the client to choose between then, not allow the client to go off looking for anything and everything they feel may work. You need to ask "Out of these three, which do you like better?" not "What font would you like to use?" -- Directed choices rather than open-ended choices.
Looking at the three fonts you cite in your question....
The general thing about all three is that they are merely sans serif typefaces. None of which are that outstanding to me, personally. Moonhouse would appear practically unusable for anything other than small display type or as you indicate alteration for a small mark. I understand Moonhouse was altered and used for the primary mark. If that's the case, hopefully it's altered to a point where the actual typeface isn't very recognizable and hopefully it's just a few letters or a very small word (hopefully all uppercase without the horrible uppercase "q", "s", or "g" in it).
I would then suspect the client is asking for a third font (Sansation) because the secondary font you've chosen (Good Times) doesn't have lowercase characters. If the client wants upper and lowercase characters, then they simply can't use Good Times.
So, what I would do as a designer is listen to the the client and their unspoken desires not necessarily the specific type choice they are citing. It would appear to me as though your client is asking for a more versatile use of type rather than all uppercase, all the time. I'm somewhat guessing without seeing your actual use, but if you've utilized Good Times at all.. I know it's all uppercase and Moonhouse is just down right ugly in lowercase form. Chances are, the client won't ever know the difference between Sansation and Helvetica or Futura or Din or any other of a thousand sans serif typefaces.
I would find a sans serif typeface which has both upper and lower case letters and works well with your primary mark image. I would dump Good Times as a choice entirely. It offers very little in terms of necessary characteristics for a "tag line" and in fact, the broken strokes, and all uppercase aspects of that typeface would decrease readability in a logotype.
I'd find three sans serif typefaces and mock up the logo using all three as the tag line typeface. Play with varying weights rather than typefaces. Set the main tag line in TypefaceA Black, then the secondary tag line in TypefaceA medium italic - that sort of thing. Be aware, if you are restricted to using free truetype fonts, you may not find many with face variations suitable for use. It may mean you need to invest in some better typefaces so you aren't restricting yourself in the design.