I may be in the minority here YTA here. For many of the things you said, like choosing to plan the wedding at a destination, etc. you're totally NTA; but one of the first rules of etiquette is that before you set the date you make sure that your close family can be there, if you want them there. Other people's lives continue on, and they may have unavoidable conflicts, even if you are getting married. It's not like the world just stops and people can just go to Italy at literally anytime just because you're getting married there.
YTA for not checking if they could make it on this *huge* trip at the time when you wanted them to go. If you don't do that, it's valid for them to feel that you didn't care enough whether or not they could make it, to even check if they could. Which it honestly sounds like you kind of don't care -- if your parents can't go, who cares about those 40 people who RSVP'd! Why are we even pointing that out? They haven't bought tickets, because they can't go. You didn't check with them before planning the date, because you expect that they can drop everything in their lives to revolve around your schedule. They have every right to be super hurt because you didn't think to make sure they could attend your big day.
Yes, this will be a huge issue for years to come. I would consider cancelling and moving the date, whether or not you can get your money back. Maybe I'm extreme. But your mom will literally be angry with you, and you'll be resentful at her, for the *rest of your life* if you don't. That's not worth it. So at minimum, just try to show some empathy that your brother won't be able to go to his own sister's wedding, instead of being angry at your family! You're mad at your Mom for being mad that she can't attend your wedding! No wonder she thinks you don't care -- you never even told her that you really want her there. TELL HER NOW if that's how you feel, because based on your actions, she validly doesn't know that. It may save your relationship.
Put differently, weddings are huge things not just for you, but also for your families, who are joining together as well as you ... Of course yes it is your day! But that day can be and is often SUPER meaningful for many other people other than just the two of you. As it should be. Marriage is a huge commitment. The important people want to be there for it. Provided you have any sort of non-totally-dysfunctional relationship with them, treat them like that's how you feel about it, too. For someone like me, that included helping out our best man to make it to our destination wedding financially, for making our wedding on a Sunday morning so that people could fly in/out and not miss work if they didn't have vacation. That level of accommodation no one expects, of course, but I'm just giving you an example so you can understand why your parents feel like you don't care about them.
But YTA for not even checking that your dates would work with your own parents before booking a wedding that will require people to take at least like 4 days vacation to another half of the world, and reacting angrily instead of sadly that they couldn't go, as if their entire schedules revolve around yours, as if they don't WANT to go to your wedding ... when practically, you didn't care either way and you're just going ahead with your plans regardless!