I have 2 fab daughters. 1 is almost 7 and 1 is 6 months old.?

my oldest daughter is from a previous relationship.. she has never met her day.. i met a lovely man 4 years ago and we are now engaged. and 6 months ago we had our daughter.. He is brill with both of them treats them both the very same and is such a good dad to them both.. our life would be great only for his mother. since our baby was born she treats my eldest badly she seems to be always giving out to her for nothing also when she texts she only says 'how is baby i am going to come over to see her today'.. i have kept my cool so far but i cant see me being able to do this for 2 much longer. my partner says she doesn't mean anything by it. it is driving me mad and i really don't know what to do it is very important to me that my kids are equal i don't believe in having favorites .. please help