Schmitt trigger design to control lead acid battery charger
This might not be efficient, but works.

You can go for a voltage reference IC like this one.
This can be used as supply voltage for your Schmitt trigger IC alone. You can scale down the threshold of 13.8 V and 13.0 V to 4.6 V and 4.3 V respectively (or any other values), using high value resistor divider at the input side of the Scmitt trigger(So that, it doesn't waste current there). The UTP and LTP are now referenced to an independent constant voltage reference from the IC. The inputs however will vary depending on battery voltage.