A.L.
umm you are in a bit of a pickle here... It's definitely hard to NOT wanna speak up and tell your sister off... that would feel great wouldn't it? :) However... sigh... in the best interest of your daughter and lessons needing to perhaps be learned, you might have to try and take somewhat of a high road..
Brace yourself ahead of time knowing that your sister is full of herself on the one hand, but on the other.. when people have to brag so much or ALWAYS be right.. then don't you think they are probably a bit insecure. Deep down she must be, otherwise why blame everyone for everything.. As you say, you don't want to hurt your mother..but you could lay down a few ground rules with your sister. get tough. you may have to and say.. look we NEED to get along... and that perhaps she could not speak her mind so much if it might hurt another.... I am definitely one for being DIRECT... but I choose my battles (like on here for example :):) however, IF invited to another person's home, that is THEIR territory and one needs to be respectful.. in other words, your sister needs to respect OUR home.. that may take your reminding her of this..
I wish you the best..