This sounds like a much bigger family dynamic problem than this one little child.
Is this child your late husband's biological grandchild, and your daughter has always held resentments toward your marriage and his family?
I don't know that there is much you can do at this point.
I am raising my 6 yr old gradaughter,have had her for 5 yrs, my daughter that is 42 yrs old disowned me today because she is so jelous of the 6 yr old.What to do?
sya, I agree with Annie. This is really a very unusual family dynamic. The jealousy of the grandma sounds curious enough, but the jealousy of the gerbils and dog really point to a problem somewhere.
I wonder what her relationships are like with her girlfriends. Does she have the same jealousy problem there?
It sounds like family therapy would be the way to go - so the therapist can watch the interactions between you, your husband, and your daughter.
Best wishes.
Given that she seems to have this behavior whenever some new living thing arrives, it might be a good idea to consult with a therapist about the issue. It's better to nip insecurities in the bud than to let them go on and on and become a lifelong problem for her. If she was in fact jealous of gerbils, that is worth asking a children's therapist about.