As far as I know it is pretty well settled that women's daily obligation to pray, when all is said and done, ends up being pretty close to men's (with the exception of ma'ariv). See Brakhot 20b with Rashi and Tosafot; Shulchan Arukh, Orah Chayyim 106:1 (with Magen Avraham and Mishnah Brurah); Arukh HaShulchan, Orah Chayyim 106:5-7. The Mishnah clearly states that women are obligated in tefilah [prayer] (it's unclear whether this is referring to sh'moneh esrei [or Amidah] as the term is generally used in the Talmud, or to some broader category of prayer), but exempt from reading the Sh'ma.
What exactly the obligation of tefilah entails turns on whether the basic obligation is d'oraita (from the Torah) or d'rabbanan (rabbinic), [and upon] one's girsa (version) in the Gemara and one's concomitant reading/understanding of that Gemara.
The upshot is that minimally women are obligated to pray a minimum of once a day (following Maimonides' and Rif's approach to its logical conclusion) and a maximum of twice a day (following Rashi and Ramban to their logical conclusions). (Ma'ariv was initially optional everyone, but men have since accepted it upon themselves–kiblu allaihu.) Even though women are exempt from Sh'ma, it is "recommended" that they say it, because it involves accepting the yoke of heaven. (See Mishnah Brurah).
Saying sh'moneh esrei drags along with it the brakhot following Sh'ma, as well, because of s'michat geulah l'tefilah (having the brakhah of redemption immediately adjacent to sh'moneh esrei). As far as I know there isn't really a greater obligation on men to say p'sukei d'zimra than on women–it's just kind of a warm-up for tefilah (which halakhically is sh'moneh esrei) and all the other stuff we say is basically "filler" too. Nor as I understand it do men have a mitzvah hiyyuvit (positive obligation) to daven b'tzibbur (with a quorum), although every effort should be made to do so. [I'm not getting into Torah reading issues here].
The only way out of all this (we're basically up to a full davening at least once and by many opinions twice a day) is by relying on the Magen Avraham, who, in an attempt to explain why "the custom of the majority of women is not to pray," says that since according to Maimonides the obligation of prayer is d'oraita without any fixed time or form, women can fulfill their obligation by saying a few words of shevach (praise), bakasha (request) and hoda'ah (thanksgiving) in the morning. (Shevach, bakasha and hoda'ah are the three essential components of prayer. Our sh'moneh esrei is therefore structured accordingly.)
In order to use this rationale, the Magen Avraham has to assume that when the rabbis transformed the timeless/formless prayer obligation into a time-bound/pre-drafted one, they imposed no additional obligation on women. In any event, it is clear from the Magen Avraham's language that his statement was meant to be a justification of the prevailing custom, rather than a p'sak (ruling) for a l'khatchila (ab initio) situation.
So that brings us full circle to the sociological/cultural aspect of this whole deal. It is true that even very observant women often tend not to daven, as noted by the Magen Avraham. Can we say that this "custom" has somehow transformed the obligation out of existence? I'm not sure that (a) this really qualifies as "minhag" (custom) and (b) even if it does, that this minhag can be used to wipe out a positive obligation (even if rabbinic). Is that how "minhag mevatel halakhah" ([the principle that] a minhag can wipe out a halakhah) is used? Moreover, it's one thing to use the Magen Avraham as a post-facto justification; quite another as a l'khatchila ruling.
Of course, the issue raised is a good one. The fact of the matter is that it is nearly impossible to daven with little kids around. So does that mean that it's ok to rely on the Magen Avraham or does that mean that possibly our community should think harder about what it encourages and discourages–and encourage men to be better about dividing responsibilities in such a way that women can daven too. And just as an aside—I have observed that when kids think it's OK to bother mommy while she's davening, but not daddy, it's largely due to messages and vibes sent out by the parents themselves.
It may be true, as a sociological and cultural matter, that the Orthodox Jewish community does not have the same expectations vis-a-vis women as men with respect to davening. And as a practical matter, the fact is that far fewer women than men daven regularly. However, let's not confuse this with the halakhic issues involved.