The main thing I feel bad about is that the OP's parents wouldn't let her do things the way she wanted to do them.
I help MIL from afar (she's only 25 minutes from here, but her treatment of me for the first 8 or so years of DH and my relationship really soured me on face-time with her, so I rarely actually SEE her), and for awhile I tried to do exactly what she wanted. But it rarely worked. So I just started doing things the way they had to be done. Things got done, she didn't actually need a play-by-play, and it all worked out. Insurance is a big one. I changed auto/renter's insurance b/c of dealing with a nice guy at her agency, and since they know that, they let me call in about her insurances. It's very convenient. But at the beginning, she *insisted* that I only talk to Pete. Well, the agent I originally talked to was Karl, and he's a lovely fellow...so do you want me wait a day or so in order to talk to Pete b/c that's who FIL set it up with years ago, or do you want me actually get it done TODAY? And frankly, after dealing with Pete (I now just talk to the person that answers), he might be above Karl, but he's not the one that gets things done correctly the first time! So now I just tell her that things are done, and don't bother trying to explain, again, why I'm not talking to her preferred person...
So in your case, depositing the check into your account a few days later, and giving the cash over to your dad that day, probably wouldn't have actually been noticed, at least not until the statement came. But things got done, and quickly, so by then he might not have cared.
Anyway, trying to follow the letter of the parental law is likely what amped up the negativity of it all for you. If it had been *your* idea, or you didn't have the money in your account to float to him, it might not have been quite as annoying as it was. (though it does sound annoying!)