Make a list of everyone you want to invite, that way, if your MIL throws you a shower, make it a point to say "please invite these ppl as well as they are very close to me and would appreciate their presence at the event". This is YOUR shower, and DH paternal side of the family should be invited- whether they get along or not. Also- . She is right- a lot can happen during a pregnancy, but you must do it at a time of your convinience, not hers.
Should she reject it or give an excuse, I guess its open season to have either your Mother or sister throw one just for your family. Your MIL has no recourse and will understand the reason why a second pary was held.
As for your own family throwing a shower, nothing is more comforting that being with people you have grown up with or people you have know all your life. Perhaps their shower will be very different than the one your DH's side of the family will throw. I would say yes. Twice the gifts and twice the fun and twice the advice the way i see it!,
" my family doesn't understand the tradition of showers (we are not American)"
My
room mate in college had a similar situation- her in laws (also
originally from india) did not underdstand what a baby shower was or
its real significance. She did some research with her DH and found the
equivalent was called a "godh bharai", and the moment she uttered those
words, it was like an "a-ha!" moment for her extended family, and they
understood!.