I want to keep the same stack (ESP8266) for code compatibility, but what I have discovered :

• The remote needs to be children proof. My girls are using it for the small robot. The 1st proto is "too big" for them. I need to remove R6 batteries, and use something slimier (3.7V battery ...)
• 3 buttons is "OK" : 1 action button + 2 left / right buttons. Pressing left + right add option menu. But all the debouncing needs to be done, and I need to add more and more sub menu for every features. More buttons is better
• The screen is quite good, and with color. But I can use something cheaper (this one cost +20$) and smaller
• No need for status LED, the screen is enough
• I wanted to be able to read pictures or details from the SD card but it's not usefull

So I will start something simpler, and I have found an amazing board for this : the D1 Mini X-Pad from amazing ꝺeshipu 

I will use :

• The X-Pad. I love the form-factor, it seems more child compliant than arduboy-like button boards, and stay very, very small
• 1 D1 mini lite (1 MB flash with ESP8285). It's a cheaper D1 mini. CPU core is the same, and I don't need flash space for now.
• 1 D1 mini Oled shield. Yes this screen is very small and black and white but it's also cheap
• 1 D1 mini battery shield
• 1 Lipo 3.7v / 400 mA battery

So it's just an assembly of standard boards :-/ Total price is well bellow 15$

But for 3rd prototype, maybe I will try to create my own PCB ...