For the sake of giving you a different slant and disagreeing with 50% or so of the replies, i'll reply to the topic question, i'll disect what you've wrote and then you can assume i'm 5% right since 19 (random guess) other people believe this woman is wrong and the devil.
I do sympathise and hope things work out. I'm also glad you're feeling better. Also i absolutly don't want this to offend in any way at all and ideally maybe you'll realise something and work things out.
Ok so:
DH and his brother don't get on, boiling down to BIL's jealousy of DH since they were children. Because he feels inadequate and is insecure.
This is insanity, many many brothers don't get on. To simply have pinned everything on jealousy is to avoid the fact that some people will dislike you even if you are perfect.
Your bil got drunk at your wedding - his wife was upset <fairly common>
Why would it possibly matter who got married first? It's not a race.
It's awesome you make an effort, it also says more about you that you can make these efforts through you grinding your teeth (perhaps needlessly?). You then say they keep you at arms length because they are jealous? That isn't the actions of jealous people. You obviously just don't get on and that's fine, but it's 50-50 and this is why:
You and her act the same, you are at her wedding (nice of her to invite you), you make a nice greeting (also nice), she talks to someone with her back to you (not good), you don't say goodbye (not good) and then text her a few days later (nice), she doesn't reply (she's on her honeymoon? i'm not taking a phone on my honeymoon and if i did, emergency only everyone can wait.)
she sends you a thank you card (not good enough 'tone') you reply (decent of you) she feels you're rude.
She says she holds her thoughts back (not good) < this is exactly what you are doing.
You have not created this ill feeling on your own, but surely re-reading what you've wrote there is alot of 'ill feeling' that you hold. Your Dh appears to be fine with the fact they won't get on and it's good he can still hold a conversation with his brother, maybe you need to do the same. All relationships are the same, some are simply not compatible and this is one of them. All this talk of jealousy is seriously flawing your analysis on this situation, you and your sil seem very alike.
Anyway, i hope none of that is taken offensively (i know it can seem that way as it's not what you are expecting). But honestly i hope you have a realisation and are happy with that and maybe moving to a more positive place than being in denial. Also i've spent more time thinking through your situation than anyone here aside from you and tried to give a logical view.
I really would like to make clear despite disagreeing i honestly hope you have a lovely pregnancy and everything works out amazingly for you.
x