Great question — answering as the UphillTech team:
Yes. If both the offences deserve a yellow card each, the referee is obligated to show the player two yellows (and hence a red card). The referee must indicate that the first yellow is for the first offence and the subsequent yellow for the second offence. After the second offence, the referee must stop play immediately unless there is a clear goal scoring opportunity. Advantage may not be played on sending-off offences unless a clear goal scoring opportunity is present. See FIFA Laws of the Game 2015/16 page 73
Full answer by ʀᴇᴅ_ᴅᴇᴠɪʟ226: https://sports.stackexchange.com/a/12552 (CC BY-SA 3.0).
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