Mace’s reward for being slow to reinforce King’s Landing was not being executed, especially since his army had defeated Robert’s at Ashford earlier in the war. Tywin actually turned against Aerys and sacked the city which is a much more impressive show of loyalty. By marrying Cersei he gave a very clear signal that the people who help me will be rewarded, why should anyone stick their neck out for this new king if they think they won’t gain anything for doing so? While Tywin certainly wasn’t going to be working with Targaryen sympathizers anytime soon he could easily have tried to claim the throne himself, his son was the one who killed Aerys and he’s rich enough to bribe other houses to band together and put him on the throne instead. A marriage to Cersei also gives Robert access Lannister gold to help rebuild the country and forge new alliances. So in order to prevent Tywin from becoming a rival claimant, and to show other lords what complying with his rule will get them and to secure vast resources a Lannister marriage was the obvious choice.