I think you need to explore WHY you feel like choosing Elizabeth to honor your DH's mom would make you feel like you are dismissing your mom. I think it would be really hurtful/weird to make a point of telling people (esp your MIL) that the only reason you went with Elizabeth is because it sounded good.
Why not let your DH honor his mom? If your mom feels left out, tell her you plan to honor her or your side of the family with your next child's name. I think Reagan Elizabeth sounds nice together!
Sorry, just had to toss in my 2 cents!