Why did a new alumnae chapter form, rather than those women joining your chapter? Was it geographically necessary? If that's the case, then they shouldn't "recruit" for their chapter - as the women graduate, if they live in (example) the north side of the city they'll join the north side chapter, and if they live in the south side of the city they'll join the south side chapter.
If it formed for a reason other than geography, maybe the best thing to do would be to get the 2 alumnae chapters together and make one strong chapter rather than two in competition.
PM me if you want, I think I might know where this is going.