TL;DR version: No, you can't do this with a single access point. It just won't work as you hope.
If interested, keep on reading for a brief description of why it won't work.
802.11n access points make use of MIMO and multiple spatial streams. As such, each antenna is dedicated to one spatial stream (i.e. antenna 1 = first spatial stream, antenna 2 = second spatial stream, etc). The second spatial stream is only used in conjunction with the first spatial stream at higher data rates, it doesn't function independently.
What this means is that if you have one antenna inside and one outside, you will either have single spatial stream data rates either inside or out, but then no connectivity in the other location.
In the situation you describe, 802.11n won't work.
With 802.11ac Wave 2 device, you do have multi-user MIMO (MU-MIMO) which allows the access point to split the spatial streams between multiple clients at the same time. While one might think this would allow the situation you describe, MU-MIMO is actually very complicated and requires the antennas to be at fixed distances from each other. So by moving antennas outside, this will simply break this feature.
In the situation you describe, 802.11ac won't work.
If you go with an older devices, such as 802.11g, these did not use MIMO. When these devices had two antennas, it was for diversity. In other words, it only used one antenna, but it could switch between which antenna it used to try to get a better signal. However even in this case, it wouldn't work well as typically there was a "delay" between when it could switch from one antenna to the other and back.
In the situation you describe, 802.11g may work in a best case scenario, but with serious performance issues.