That is very interesting. I only read that Maria Carolina was the only one given the chance to sit in the privy council after she gave birth to the heir. Marie Antoinette never really was that into politics than having a good time (balls, dresses, jewels & favorites/lovers). I think Maria Amalia was in the middle perhaps, since she was not given a clear political role in her marriage contract (unlike her sister).
Yes, it was only Maria Carolina who had that clause in her marriage contract, neither Marie Antoinette or Maria Amalia had the same privilege. But MC interfered early on and started clashing with Tanucci over various matters. There's not much difference between Maria Amalia, Maria Carolina, and Marie Antoinette in this respect, all 3 interfered whether they were given the explicit right or not. Maria Amalia indeed wanted to rule in the early months but she didn't have any formal role. She gave up the idea (of ruling) quite fast, what she subsequently wanted was for husband to rule (not France or Spain through Du Tillot and Del Llano). We see that she stuck to her resolve later on, she dropped out of politics mainly. So she was sincere in her wish to have Ferdinand a free hand in his duchy:
"I want nothing more so that he can enjoy public esteem...". Of course, she didn't feel shy asking her husband for this and that later on, but mainly she dropped out of it.
For a time both sisters (Maria Carolina & Maria Amalia) operated independently through their willful ways (the lack of strategic ways, but by outbursts and pestering their husbands). Maria Carolina worked closely with what Austrian interest (hence the approval of MT) while Maria Amalia (as most historians seem to indicate) according to her personal likes and dislikes of the person/ministers.
I don't think Maria Amalia needed to bully her husband (as much as Maria Carolina did to her Ferdinand) regarding Du Tillot. I can only think of one clear instance when she forced his hand on this. We have to remember that as much as Maria Amalia disliked Du Tillot (and she truly hated him), her animosity was
lesser than her husband's. Perhaps Ferdinand couldn't bring himself to defy his grandfather Louis XV and his uncle Charles III so openly but Maria Amalia didn't share his hesitation. While Du Tillot was portrayed as an enlightened minister who made many reforms and made Parma a great cultural center, we have to keep in mind that the locals (except for his favoured local nobles) were quite left out of it, and the good results of reforms passed only came in trickles... very slow in coming. In the meantime, Parma was saddled with a staggering state debt of 31,000,000 liras, a big chunk which was due to his "reforms" and "ambitions". The people greatly resented that. It was a clearly a question of who actually benefited from his administration.
On top of it all, Du Tillot wasn't to be trusted as far as the duke and duchess were concerned: there were unsatisfactory answers to what he did with some of Ferdinand's personal money (the cash inheritance Ferdinand got from his grandmother Elisabeth Farnese); another issue was his instructions to the head of the archives in Piacenza to destroy certain documents so as to favour the family of his mistress Marchesa Malaspina over some inheritance issue. Maria Amalia and Ferdinand couldn't also be blind to the fact that Du Tillot slandered her at the foreign courts (no doubt including the stories about alleged affairs with bodyguards, of which there is no concrete proof) and made it appear that Ferdinand wa someone who "amounted to nothing." We need to get hard facts like that (aside from Ferdinand being offended at Du Tilot's anti-clerical policies and Maria Amalia's willfulness) to understand why Maria Amalia and Ferdinand wanted to get rid of him.
On Del Llano, so far I think it was only Maria Amalia who disliked him, not Ferdinand. So in this particular minister, she seems solely responsible for his dismissal and the political mess it created. But to be fair, she was also motivated by her wish (and Ferdinand also wanted it himself) that Ferdinand would be the real ruler of Parma, not someone else controlled by France and Spain. We have to remember that Ferdinand never blamed Maria Amalia for any of their troubles - even when their families cut off correspondence and their appanages - and he seemed grateful to her for taking the flak from everyone else.