I have a circulating system that works without a pump, so I'll not say
anything about the pump, other than that I assume it is plumbed to the
bottom of the water heater. Incidentally, the two plumbers I have had
work on my system, while licensed, didn't know anything about how the
system worked, and one even installed the check valve backward.

My guess is that you don't have a functioning check valve, so when you
turn on the hot water, you draw both hot water from the top of the
heater, and cold water from the bottom. That would explain why the line
near the pump is cold. I would suspect the shower that is nearest the
line drawing hot water from the top of the tank would get mostly hot
water, while the shower that is nearest the return line drawing cold
water would get more cold than hot water. Its possible that when using
only one shower, you get enough hot (even when mixed with some cold)
that it feels hot, while when using both showers you are drawing more
water, and get the imbalance you describe. I know my system worked
without a check valve, but I got hotter water after I added the check
valve, and got the plumber to point the arrow the right way.
Incidentally, when he came back to redo the check valve, he said he had
been talking about my system with some of the other plumbers, and they
weren't certain it would work, so at least some of them knew about it.
Mine works without a pump because I have an old house with about a
fifteen foot vertical rise from the heater in the basement to the
upstairs bath, and I insulated that rise, while leaving the return
uninsulated. Thanks to gravity, the hotter water rises naturally and
the system works.

wrote:

just wanted to check if I have diagnosed this correctly.
When hot water is being drawn used in the house
(like in a shower) the inlet to the recirc pump, which is
next to the water heater in the garage, starts to run very
cold. I assume this is not normal and must mean that the
recirc pump is broken in some way?

my issue is that when taking a hot shower in a bathroom that
is closest to the water heater, the water turns very cold in parts
of the house that are further from the water heater (but closer
to the return pipe for the recirc pump). i.e. water in one shower
is nice and hot while water in the other shower is very cold
when both are running. the "cold" shower returns to nice and
hot when it is on by itself. I replace valves that could be causing
mixing and/or turned off secondary shutoffs and nothing worked.
Only thing I notice now is that the return pipe going to the recirc
pump gets very cold when I have both showers on and then one
of the showers run cold.

is there anything else i should try to make sure its the recirc
pump or not? My water heater is less than 2 years old and since
I get steaming hot water during this problem I assume its not the
issue.
recirc pump is 9 yrs old.