luke warm water after tapping new pipe to water heater

[Shu Peng]

I understand this forum is for DIY and I have obtained help twice from here for DIY projects. I do not have the energy to DIY this project so hired someone to replace a water heater.

my master bedroom shower has a separate small water heater and is broken. Plumber suggested we hook it back to the big tank to save energy, which made sense and we agreed. He tapped the cold and hot water pipes close to the water heater  cold and hot water supply (near the top of the main supply line). I guess it is easier than locating and reconnecting the original water pipes. After that, most hot water line only have warm or cold water. The master shower and kitchen has hot water. I suspect the way or the location where he added the new pipe caused the problem but of course he insists he did nothing wrong. He added the hot water pipe on a T junction and hot water is no longer going down the pipe and only flows to the horizontal line (see picture). The main cold water supply is as hot as the hot water supply to the heater. I am concerned.

is it possible that the new hot water pipe for the shower (lower white pipe) is tapped in a wrong place and causing hot water not going down to the vertical hot water pipe? it feels luke warm while the horizontal line feels hot all the way down. The luke warm pipe is probably responsible for the rest of the house hot water supply.

should he tap the new pipes down somewhere else instead?  The plumber is a nice guy but It seems to me that he does not know how it should be connected to the water heater. I want to check here, hoping to learn the correct way to reconnect big water heater to my shower.

[Shu Peng]

I don't see a place to edit my original post. here are some updates:

now all the fixtures only have lukewarm water. The hot water I had for shower and kitchen was probably from before the fix. 

I realized the new cold water pipe is not sending to shower. The plumber hooked the cold water line (that was supplying to the disconnected old small tank) to the big water heater, basically adding an extra cold water loop to the cold water line. I don't understand why he did not just abandon that cold water line and cap it off. He is saying that add more pressure and make water flow faster.

The plumber told me that the big water heater was set to vacation mode and asked me to turn to setting A. I don't know how that would happen as we were having hot water. We never touched the setting since he installed for us last year. Vacation mode won't give you hot water, right? it is odd. it is now set on B, 140F, but the water is still lukewarm.

Is it possible somehow the heating element is damaged and it is not heating water properly?