Does anyone know how SQL Server determines the order triggers (of same type, i.e. before triggers) are executed. And is there any way of changing this so that I can specify
You can use sp_settriggerorder to define the order of each trigger on a table.
However, I would argue that you'd be much better off having a single trigger that does multiple things. This is particularly so if the order is important, since that importance will not be very obvious if you have multiple triggers. Imagine someone trying to support the database months/years down the track. Of course there are likely to be cases where you need to have multiple triggers or it really is better design, but I'd start assuming you should have one and work from there.