Structure satisfiability and entailment

Let $$Fv[\phi]$$ be the free variables of $$\phi$$. Suppose there are 2 formulas $$A,B$$ such that $$Fv[A] \subseteq \{x,y\}$$ and $$Fv[B] \subseteq \{x,y\}$$.

Prove/Disprove: $$T \nvdash A\wedge B$$ iff there exists a structure $$M$$ such that $$M\models T \cup \neg(A\wedge B)$$

I'm pretty sure it is wrong. My reasoning is that if that even though there is no structure such that when $$M \models T$$, then $$M \models A \wedge B$$, that doesn't necessarily mean that there is no variable assignment $$v$$ such that $$M, v \models A \wedge B$$. So what we need is formulas such that for each structure $$M$$ that models $$T$$ there exists an assignment $$v_1$$ such that $$M, v_1 \models A \wedge B$$, and also and assignment $$v_2$$ such that $$M, v_2 \not\models A \wedge B$$. However, I cannot find such formulas and I'd like an example.

thanks

$$T= \emptyset$$
$$A = B = p(x)\vee\neg p(y)$$