As has been said before in other comments, and from my own difficult personal experience, don't give in to his mother (or parents in general) because it will set a precedent. She will then expect to be consulted and have a vote on every single aspect of your lives - where you live, work (or even if you should work), naming your children, how to raise them, how much time you spend with your parents and probably what knickers you put on in the morning. Oh, and if you celebrate Xmas, that will become a nightmare too. Don't give in. You don't have to be rude about, just as long as you are both consistent. She wants a reason to blame you and convince herself that her DS wants her to interfere in his life. You are the one throwing a spanner in the works.
For what it's worth, whatever you'd chosen to have on your wedding day would have been wrong. If it was more extravagant, she'd just call you a gold digger. Even if she did have his wedding day pictured in her head, I suspect her real problem is that she's not the only woman in his life any more. She's trying to get him to change plans, not necessarily because she envisaged a perfect wedding, but because she wants him to choose her over you. It's about insecurity. If he gives into her, there's a chance that her demands will become more and more outrageous as she demands more 'proof' he loves her.
Unfortunately I experienced this first hand. Firstly, my then future MIL blamed me because he bought himself a flat and left home. He was 24 at the time, so a mere baby who still needed his Mummy. I was an evil influence apparently, even though I was only 16 and didn't know it was even possible to buy property as I came from a council estate and didn't know what a mortgage was. Four years later, she had a meltdown and made us change our wedding date because his brother couldn't make it. Changing plans would have been much easier for him than for us and I don't think I was BU in wanting to choose my own wedding date. He was on my side until she started crying. So we changed the date, meaning my brothers were unable to attend. She cried the whole wedding day because I'd taken him away from her. It was . Ironically, I didn't even want to get married, I was doing so because I was pregnant.
She decided before my son was even born that I was too young and wouldn't be able to cope. She thought we were just going to give her our baby (so did my mother, but that's a whole other story). I disabused her of that notion and she started screaming at me, then at everyone around her. After she calmed down, she then behaved as if I had the mental age of a 5 year old and told ME not to be so silly, of course she would have to raise our baby. I said the answer was still no and she let rip again.
When we had a daughter, she expected us to give our daughter the name she would have called a daughter if she'd had one. This was without even consulting us. I told her that it was nice of her to be thinking of us (it wasn't), but we'd already chosen a name. She cried, she shouted, she phoned relatives and told them how utterly heartless and unreasonable I was being. You name it she did it. I stuck to my guns as I hated the name she wanted and she never forgave me for it.
You'd also expect someone of her generation to want things done by the book, like children having set bedtimes. On one visit, she did everything she possibly could to delay their bedtime (they were both under 4 at the time) and in the end it was 9.30pm and they were both crying because they were so exhausted. So I stepped in and said they really needed to sleep. She complained because she wanted to spend as much time as possible with them (their needs were irrelevant). I made the mistake of letting her read them a bedtime story, so she chose the longest one she could find. In the end they were both howling because they just wanted to sleep. I had to step in because they were so distressed. She threw the book at me and stormed out of their room. She got to the living room, told my then husband and FIL that I was really mean, started crying again and had a full on temper tantrum. But I know that if I'd said they could go to bed whenever they wanted, she'd have called me a bad mother. Hell, she did anyway over everything. I'm really extravagant and wasteful apparently because I use one tea bag per cup, not one for four. I also don't put it on the washing line to dry either before re-using it for another few cups. I don't separate 2 ply tissues and serviettes either to use them as single sheets and I bought myself a small bar of chocolate once with my own money, which she found outrageous (this is the actual truth, not an exaggeration). It's a wonder he didn't get me to sign a prenup with all that high living. It's the slippery slope to a gold plated Rolls I tell ya!
Unfortunately my then husband would agree with me in private, but as soon as he faced her, his resolve crumbled. Our divorce was granted on the grounds that his refusal to stand up to her was unreasonable as her requests/interference weren't just ridiculous, they were extreme and irrational. These are the judge's words, not mine. He refused to stand up for me/us/himself/his children because she made it clear his brother was her favourite and he was scared she would withdraw the little bit of love she showed him altogether. So she made him jump through one hoop after another even to the detriment of his own children. It made all of our lives an absolute misery. The irony was that I was always polite and respectful to her (even if I was saying no and not backing down) and she never extended the same courtesy to me. My children had to witness her behaviour and see her treating me like something on the bottom of her shoe, no matter how nice I was to her.
In your case, as for this 'showing [you're] taken' thing, is she implying that you are unable to simply tell people you're 'taken' (a horrible way of describing your engagement), or is she saying that you intend to cheat? Is she deliberately trying to sow seeds of doubt into your DP's head? If you wanted to cheat, you'd just take it off. I mean, what difference does it make to her if you have an engagement ring or not? But you know if you were the one who wanted the ring, she'd be tutting at the amount spent on it. You can't win. You'll never be able to win.
At the end of the day, it's your wedding and your call. It sounds beautiful by the way as it shows how much you truly love each other. What's important is the vows you're exchanging and not the extraneous stuff. That's not to say that those with big weddings aren't in love. It's just that I had a friend who was so caught up with 'the day' she forgot about 'the marriage'. They separated after 9 months, were divorced within a year and were still paying for their wedding (they'd taken out a loan) for 4 years after they were divorced. Stick to your guns and have a marvelous day, just make sure she knows it's what you BOTH want. Otherwise, she will happily dump it all on you. Congratulations and good luck 🍾 💘 💑 🎊 🎉