It very much sounds to me as if Shanavine resents how much time the SO's daughter needs, eating into the time he(?) gets with his partner.
Unfortunately, it sounds as if the daughter needs the support of her mum. So Shanavine, you can stay and tolerate it, trying your best to add no extra stress to the daughter. If you cause any of the stress already, OR if you add to it by being pushy or resentful, it sounds as if it'll just push your partner further away from you.
Or of course, you can leave. If you really can't bear to tolerate it. Because since you're not the father, you don't get a say in how the mother acts.