All tankless use a system to detect flow, and only turn on when that flow exceeds a certain value (differs by brand and model). You may have a super saver showerhead, or you like it cool, because it sounds like you aren't getting the flow needed to keep the thing turned on. That's why, when you also turn on a sink, the increased flow triggers it to turn on. You might try a different showerhead.
A thermostatically controlled shower valve is nice, but it can't magically generate hot water...if it isn't coming in, it can't adjust. But, if the temp varies while the shower is going on, it will try.
Also note that many tankless systems have a flow restrictor in them, and this can mess up both pressure balanced and thermostatically controlled valves. Read the info carefully, and check with the manufacturer before investing in making a change.