Joffrey was immediately the king once Robert died. I don't think age has anything to do with it. Cersei was the Queen Regent only because her son hadn't married yet and they were waiting for a suitable queen, the prime requirement being able to bear children. I'm thinking that not only does Tommen get to immediately be king, but that Lady O completely thought this through and knows this and intends for Margaery to wed Tommen as soon as possible. Tywin, who's really making the decisions has no reason not to agree with this. All of his alliances and arrangements would remain the same.
As for consummation of the marriage, yeah, I do agree that this may be brought up but I don't think it will mean much "for the good of the realm/family/whatever". It will probably just mean that Margaery is not the queen/without power right now, but will facilitate getting she and Tommen hitched. I'm sure Lady O will bring up already having paid for half the wedding festivities as added incentive that Tywin owes her.
The only enemies Tywin/Lannisters will have left in terms of he not paying any attention to them are Daeny and Littlefinger (who I personally think is the character who gets to take down the Lannisters - all that dialogue over time about the banks and how Littlefinger took out all those loans for the realm.) He left Tywin essentially with the bill while he's off to the Vale to move onto the next part of his plan of world domination. Westeros is in debt (since even Robert's reign as commented by Ned). Littlefinger has been playing the long game the entire time gradually bankrupting the realm. Combined with winter coming, I believe his plan is for the people of Westeros to revolt with little food growing to go anywhere or being burned stupidly, completely destabilizing the economy with the debts he created meanwhile having pocketed a lot of the money which he can continuously pay his own army (Lyssa's...Varys even comments that its the one thing left that he needs to rule) while the other armies of Westeros abandon their posts and allegiances because they're simply not getting compensated anymore. This dissent has already begun as we see with the Brotherhood Without Banners and that poop being thrown at Joffrey. Also it adds a bit of poetic justice for Littlefinger to use the one thing the Lannisters value the most as their undoing. Either it's him or some surprise Reyne that survived and bred. I forget which character, but someone even mentioned once how all these tournaments, weddings, etc. need to be so lavish and entertaining because it serves to distract the masses from their minds wandering towards their own injustices.
Tywin isn't just going to let his plans with the Tyrells vanish. He needs them and the Martells for their money and southern agriculture. So he has to be or get on the same page as Lady O with Cersei+Loras, Tommen + Margaery, Myrcella + whoever/Martell seat on the council.
Speaking of other enemies. I guess Tywin isn't worried at all about the Greyjoys and just a little bit with Stannis. I don't even get who Balon is fighting. As far as I can tell everyone else has been busy fighting everyone but the Greyjoys. He must be just sailing his boats in circles killing fish.