I'm going to have to agree with the other posters here-- Finding a 2 bed flat in a nice safe, family-friendly area with council tax and your travelcard included for under £1500 pcm could prove difficult. Including utilities in this would be closer to impossible.
Somewhere on the District/Piccadilly lines would suit you, so areas of west London like Ealing (Zone 3) and Chiswick (Zone 2) are quite family-friendly, given the number of prams (strollers) I used to see being pushed around there, but a quick search on Zoopla shows only a few 2 bed properties under £1250/month. Rents do tend to get cheaper the further out you get, and the difference in cost for a monthly travelcard from zone 3 vs. zone 2 is a minimal £20/month more (Z1-2=£120, whereas Z1-3=£140 and Z1-4=£170). The commute from Chiswick/Ealing would probably be 45 mins door-to-door, depending obviously on your journey to/from station.
I'm not familiar with areas further afield from here, but they could be worth looking into if you're more flexible with commute time than cost. It might also be worthwhile to start out in a shorter-term 1 bed place until you can get a feel for the different areas, and use this as a base. If your wife won't be working during her time in the UK, perhaps she could arrange viewings and get a feel for the market (I've never been 6 months pregnant, so am not sure how feasible this is...)
My partner and I were looking to move from West London to North London, to be closer to my job/share the burden of commuting. At the time, our jobs were just over 2.5 hours away from each other, and we were pretty restricted with respect to budget and search area, which was dictated by transportation links. We held out, and searched for over a year to find a place that fit our requirements, and finally did. (Unlucky for me I then changed jobs...). My point is that maybe by renting a place in the shorter term will give you both more time on the ground to find something that will suit your needs.