I think you are attaching the handles just fine, but using either the wrong handles, or the wrong size knitted "fabric". I'm a knitter who recently got addicted to sewing (mainly by making knitted bags like you are talking about...).
My suggestion would be to get bigger handles since you said that you can't convince your MIL to make a different pattern. Also, another way to attach the handles would be with the lining - there are lots of creative ways to use a tab-attach handle when you put a lining in that bag (and since it's knitted, the liner will help shape the bags and reinforce it)
Good luck with your business...I've always wanted to do that, but I seem to have grandiose plans that I never do much with - so for now, it's making bags for me and family)
I love love love it! My sister just got to bring home her beautiful bundle of joy - her first baby, a girl, who spent the first three months in the NICU because she was born at 29 weeks and was only 2 oz. - But it has a happy ending because she's now home with mom and dad doing just fine
I've just gotten into sewing with the addition of a new sewing machine for christmas (though I've been lurking here for awhile) - I have been saving all the diaper bags to my favorites...trying to get the courage to try it out! the zippers and elastic are all new to me, but she says she'd be happy with whatever it looked like