I am creating a apache module along with a shared library within the same Autoconf/Automake project. How my Makefile.am ought to be?

It is now:

INCLUDES = -I$(top_srcdir)

nobase_include_HEADERS =  \
  foo.h \
  bar.h 

lib_LTLIBRARIES = libfoo.la
libfoo_la_SOURCES = \
  foo.c \
  bar.c 

libfoo_la_LDFLAGS = -version-info 0:0:0

I'm able to add wrinkles:

lib_LTLIBRARIES = mod_foo.la
mod_foo_la_SOURCES = mod_foo.c
mod_foo_la_LDFLAGS = -module
mod_foo_la_LIBADD = libfoo.la

Could it be right?

steps to make install the module with APXS and also the shared library with libtool? Basically put:

install:
    $(APXS) -i -a -n foo mod_foo.la

I believe the libfoo.la it's not installed only the module.

Nothing's being installed because you are overriding the install target. Use install-exec-local (manual):

install-exec-local:
    $(APXS) -i -a -n foo mod_foo.la

(Observe that I'm not sure APXS, I am just copying your rule.)

It's also wise to define an uninstall-local target to wash up.