I think you have a good plan.

I suggest you buy your tickets from Berlin-Schoenefeld Flughafen right through to Bielefeld. Having this ticket begin at the airport is the same price as having it begin at the main station. That way, if you do get out in time for the RE train at 18:50 (or any later one), you simply walk on and don't worry about tickets.

As I mentioned yesterday, your last "good" train leaves the Ostbahnhof at 19:37 and the Hauptbahnhof at 19:48. So, if you get out of the airport after 18:40 and before 19:20, a taxi might be a good option. If you're lucky, you might make that "good" train at 19:48.

If you are even later, you will have to use the following connection:

Berlin Ost dp. 20:56 ICE 540
Berlin Hbf dp. 21:07
Hannover ar. 22:56
Hannover dp. 23:09 RE 4858
Minden ar. 23:52
Minden dp. 00:30 RE 10890
Bielefeld Hbf ar. 01:05

If you want to do this, there are RE trains leaving Schönefeld at the following times which will get you to the Hauptbahnhof on time:
19:22, 19:50, 20:22. Actually, all of these trains, including the 18:50 train, stop at the Ostbahnhof, so you can also change there. However, if you have a long time to wait, the Hauptbahnhof is better, as there are many stores and restaurants.

However, if you are travelling with lots of luggage and 2 small kids, you might also consider one of the airport hotels, the Meininger Hotel (which will cost you € 60 plus € 12 for the airport shuttle) or the Holiday Inn (which will cost you approx. € 100). Then you could leave the next morning and have the relatively easy connection of an RE train to the main station and an ICE direct to Bielefeld...

Good luck!