Parents being ….difficult

If you want to be completely in control, then I wouldn't expect them to help out financially. A lot of times because parents are paying for things they automatically assume or try to take control. Also why do they need to be messaging your in-laws about pricing?

Are they just financially helping with the engagement party so far? If so, and you're able, I'd kindly reject all monetary assistance going forward into the actual wedding. If you take their cash, you're going to have to hear their opinions. If you don't, you get to say, "This is my wedding, thank you, but I have it handled". If you want to, delegate a task to them. Like, let them pick and pay for the cake. They can plan your bridal shower or cultural equivalent. There, they get to be involved (and also leave you alone)

Part of them still treating you like a child does involve you allowing that behavior. You need to stand firm. Tell them "We can discuss this later, when you're calm." Hang up or leave the room. Don't go back on your word and let them keep talking at you, that tells them you don't mean it. They don't get to yell at you.

Are you living with your parents still? If so, have you ever lived on your own? Reasons for asking is if they are used to you living with them and depending on them they might be having a difficult time adjusting to the fact that you are a grown woman who can make her own decisions.

I totally sympathize with you, as I am dealing with something similar. The difference here is, my FH and I are paying for absolutely everything ourselves. Both my parents and siblings are being difficult, but we kindly tell them that "at the end of the day, its our wedding, and when we look back at it, we want to be completely happy with everything we chose. Settling/compromising for the sake of making others happy is not something you should ever have to do when planning your DW. The only opinion that matters, is that of your Fiancé.