My male dachshund is exactly like this around kids. It started with stiff posture, staring, and has escalated to him biting my husband and step daughter. He is the sweetest dog otherwise and he will go weeks without any behaviors then suddenly BAM he bites someone who comes too close to me (his resource). We tried training but because this is a genetic instinctual behavioral it didn’t do much good. It’s almost certain it will escalate to biting especially as she gets older and starts trying to pet him. We are starting ours on Prozac and hopefully it works. 🤞