How much water comes through the faucet when you turn it on? The tankless hot water heaters are designed to heat ? gallons to ? degrees. If you run more water through the temperature goes down. The shower head is probably putting out half the amount of water the tub faucet does. Letting the shower heat up all the way. Does the bad tub have a shower on it also? If so try that and see if that heats up to a comfortable temperature or just try turning the faucet on 1/4 of the way. Does it heat up?

If this is the case you may have to buy a bigger heater or put up with less water coming out of the tub faucet.

Hope I explained myself well enough.

A temperature balanced valve sometimes need to be setup. It may not be set to allow for the hottest water possible.