charge SLA battery while using it

I will add a small auxilary battery (lead acid 12V 2.4Ah) on my car for me head unit to be able to crank the engine and not turning off the system. Now, if I crank the engine while the unit is on, it will turn off due to the voltage drop of the car battery.

The small battery will be connected behind the dashboard using the cable that would normally go to the stereo. I will add a relay between the two batteries that gets signal from the alternator so the second battery won’t be connected with the main battery while the engine is off.

I found an old circuit that was using Ni-Cd batteries, two zener diodes and a resistor. I added the relay on that circuit and I came up with this

I think that D5 is there to ensure that no current will flow from the small to the large battery. R1 limits the charge current and D6 allows current to flow from the small battery to the car stereo.
Which battery will power the car stereo while the engine is running?
Is this safe?

My main question is about the resistor. How could I calculate the resistor value?
Now my battery reads 12.8V and if connect it to a power supply at 13.7V it draws about 100mA. If I connect a 10Ω resistor the current drops to 50mA. What will happen if the battery voltage drops to 10-11V? How much current will it need and what resistor would I choose to be safe?

What type of zener diodes should I use? Are these ok?
My battery is this one.