I think the problem Meghan has with Kate is that she knows how fond Harry always was of her - they had a great relationship, and he wanted William's family life for himself (not in a weird way!)
Unfortunately for Harry, there are not too many women like Kate around - neither Chelsy nor Cressida were prepared to take on the royal life. So he grabbed the first one who would - who happened to be Meghan.
Imo, Meghan is and will always be jealous of Kate, firstly due to her position in the RF, and secondly, because she knows how much Harry thought of her.
Didn't Kate unexpectedly join Harry at a Service last year, and their old closeness was evident.