With regards to monetizing the site, I would look at how the site is currently monetized. Why? Well in my opnion ads are one of the best indicator of monetization because, if they are converting well (for instance if the third party is a CPC network) then you could find a similar company/the same one and replace those adverts with CPA adverts - instead of getting paid per click you would get paid per action (generally via a purchase - although this tends to be much higher than CPC earnings - hence affiliates doing Adsense/Adwords Arbitrage etc).
Secondly, you could easily roll out a membership area (if the site doesn't have one) and offer paid memberships with certain upgrades. Theres loads of stuff you can do with the membership area to monetize your users.
This leads onto point 3, which if the site isn't already you should send a weekly/monthly newsletter to the members (if you implement a membership area) or to people who are subscribed to the mailing list (you don't even need a membership area to do this - just offer a newsletter on your site - which you can sell advertising in, as well as offering products to them again using CPA networks or your own suppliers).
Fourthly, you could roll out an iPhone/Android App (infact you could make a few "parenting" apps) and have them either as paid apps or free apps (which unless the apps provide real value added service, I would opt for the free app option which can be monetized via ads within the app although this isn't your only option).
Additionally, I saw that you said 80% of the traffic is from Google. This is a double-edged sword - you're willing to lie and die by Google - If one day Google decides to re-rank your site or changes its algorithms your site could easily lose 80% of its traffic overnight. In order to combat this, you need to diversify the traffic to the site as well as, at the same time you still need to take advantage of the traffic Google commands which means, quite simply adding more content, doing on-page seo and then focusing on off-page seo. However, if you are focusing on diversifying your traffic streams via link exchanges/content exchanges etc this will already be helping your off-page seo strategy (to some extent) so you can rank for more long-tail keywords, as well as increase the rankings of your current positions which means more traffic to the site.
With all things considered, you have a lot of potential advertising/monetization options and I haven't even touched most of the options you could implement but you should focus on growing the revenue streams as well as, diversifying your traffic stream so that your site will continue to grow and provide a nice return from your investment.