I would first test for parasitic draw in the toad. Even if you install a separate wire from the battery to a cig lighter receptacle for the toad brake. Your toad may be drawing too much current from the starting battery when the engine is off.
A wire from the MH's battery to a toad battery is not actually a power or charging connection it's mainly allows your MH to trickle charge a toad's battery while the MH engine is running. A trickle charge can take up to days to charge a battery. So if your toad battery is not at full capacity trickle charging may not do alot of good especially if there is too much parasitic draw.
This is a common problem with many vehicles, especially modern vehicles from the factory with all the additional electronics. Also other axillary devices installed in a vehicle potentially drain starting batteries when the engine is off.
What I would do is test for any parasitic draw and test your toads starting battery to determine if the toad's battery is good and also test the Mh's (trickle) charge line. I also use a load tester on all my batteries. As starting and rv/marine batteries sometimes test ok only when not cranking.
How to Find a Parasitic Battery Drain: 9 Steps (with Pictures)
My toad I have two batteries, a starting and aux, with separate circuits and fuse boxes. I keep all my axillary equipment so it works off a separate system. Trying to combined aux device with modern vehicle OE electronics imo is a bad idea. Down the road increases the likely hood of problems occurring, plus if you keep your aux device separate from your OE electrical (which includes vehicle computers, switches, relays, sensors, etc) significantly helps when diagnosing and troubleshooting.
Minimally with only a starting battery you should run separate aux. wiring with fuses. (Some modern vehicles come with a cig adapter(s) that are suppose to run directly from the starting battery. However I never trust them as their usually integrated somehow into the OEM's wiring.)
Modern vehicles aren't like older cars from the 50's (which I've owned and worked on) where their electrical wiring is mostly battery, ignition, vehicle lighting and a radio.