Electronic – “Conflict power between pins” with a voltage regulator

I think what I would do here is simply have two global supply names, one for each supply e.g. +5V_A, and +5V_B. Then you can use the standard supply symbols.

OR

Have a master sheet with all the hierarchical sub sheets on it (power supply and driver boards) and wire things up directly using the hierarchical sheet inputs. Here is an example of this (only power net wired for clarity):

Master Sheet:

Individual Sheet:

Individual Sheet with two symbols used (Sheet 2):

PCB connection:

The same hierarchical label (3V) is used on each sheet, but on the master two separate regulators are used. One supplies sheet 1, and the other sheets 2 and 3. On sheet two another IC is also supplied with a separate 3V symbol - on the master sheet you can see two inputs are needed.
The hierarchical symbol does not appear to have automatic connection, so you either have to wire it up normally on that sheet, or add as many input of the same name to that sheet as separate symbols used.
You can on the PCB snapshot (the other net is a normal global ground symbol) everything is connected correctly.

In case this is relevant - if you want to split one supply into two nets, use a "jumper" component (e.g. 0Ω resistor) so the schematic doesn't complain, so then you can have e.g. main_supply, supply_1 and supply_2 all electrically connected, but split for PCB requirements (e.g. like you might have an analog and digital ground)

OR Possibly:

Make a power supply symbol, use the # symbol in the reference designator (IIRC) which tells Kicad it's not a real component. Don't use a power flag on it though - this may work for a local power symbol if the quote below is correct (documentation is not the best though, and is outdated in some places so you need to be careful)

To quote from the link below:

A Power Symbol (VCC, V3P3, etc.) gives the net its name and is used on each page to tie to the global power net. It is a special component not listed in the BOM. A Power Flag (PWR_FLAG) symbol which gives the net its global characteristics - connecting power nets between sheets.

There is info on creating power symbols at the bottom of this link.

The solution that you have on your pictures will work fine. I have checked the Battery element in the library editor and it has both pins as a passive pins, so ERC wont complain.

If you want to use +9 V and GND elements from Power library, then you also need to add a power flag. In the reference they say:

It is common to have an error or a warning on power pins, even though all seems normal. This happens because, in most designs, the power is provided by connectors, that are not power sources (like regulator output, which is declared as Power out). The ERC thus won’t detect any Power out pin to control this wire and will declare them not driven by a power source. To avoid this warning you have to place a “PWR_FLAG” on such a power port.

So, using the power flags, you can make following configuration:

Regarding the hierarchical sheets, take a look at this video to learn more (browse the channel, there are lots of very useful videos for KiCad).