Face‑controlled 3D character for kids to talk & play live

Overview
I'm an early-childhood educator building a small prototype to use with the young children I teach. The concept: I control a 3D animated character live using my face, while a child in another location plays with that character on a tablet: talking to it and tapping things in a shared scene that respond in real time.

Nothing is built yet, this is from scratch. The scope is small on purpose, but it has to genuinely work end to end. I'm on a tight, fixed budget, so I want a lean build, not a full app.

What version 1 needs to do:
- One simple 3D room/scene, child-friendly.
- One 3D character in that scene that I control live with my face (facial expressions and head movement driven by my camera).
- The child, on a tablet in another country, sees and hears the character in real time and can talk to me through it.
- 3 to 4 tappable objects in the scene. When the child taps one, it responds (animates / plays a sound / changes the scene), and I can see what they tapped so I can react in character.
- Low latency enough for natural back-and-forth conversation.

Important and you decide the tech
I'm not prescribing the avatar or networking approach. You're the expert: propose the simplest, lowest-cost way to hit the requirements above. Tell me what you'd use for the face-driven 3D avatar (including whether we should buy or use an existing rig/model rather than build one to save cost), and how you'd handle the real-time remote connection between two countries. I want your recommendation and your reasoning.

What I'll provide
- A clear walkthrough of the intended experience
- Character and room art direction (or budget to source a 3D model, open to your advice here)

Out of scope for version 1
- Login, payments, content library, multiple characters or rooms
- Production-grade polish
- Anything beyond the single remote interactive scene above