It could be that they will both be just fine! Petra will learn to accept her as part of the family if your mom does the same sort of positive reinforcement that you guys have been doing!! Maybe your mom could have little treats around for her at special " good girl" times.
I'm so sorry that you have been ill as well. Boy, sometimes it feels like there's no end to problems, huh. That old saying, 'that which doesn't kill you makes you stronger' maybe overused, but it seems to apply here!!! Get better!!
I think sometimes dogs sense when someone isn't feeling well and it's not the time to mess around! It is so amazing that she's come so far! You guys are awesome!