It's almost certain that the reason for the immediate
disconnection is that you're answering a voice call, and not a
data call.

There are several complex issues here.

Firstly, less carriers are offering circuit-switched-data (CSD)
service.  Of those which do, some don't allow prepaid SIMs to
initiate CSD calls.

Secondly, are you dialling the receiving modem's voice number or
its data number?  If you're dialling its voice number, you've
almost certainly established a voice call.  If both SIMs are
with the same carrier, it's just possible (but extremely
unlikely) that they'll let you make a CSD call to a voice
number.  If they do allow it, you'll increase your chances of
success by selecting the V.110 ISDN bearer service with

       AT+CBST=71

prior to dialling (if your carrier supports it).

In general, GSM voice and data calls have very different
characteristics.  The type of call must be determined for both
OTA legs prior to call establishment.  The standard mechanism
for establishing a CSD circuit involves two aspects: using the
semi-colon after the destination number to specify CSD on the
calling leg, and dialling a _data_ number to specify CSD on the
receiving leg.

The provision of a data number is usually a separately-priced
option that's not available to users of prepaid SIMs.

On connection, you'll automatically be in data transfer mode.
Characters you type subsequently will appear on the other
device's serial port.  This happens in each direction once a
connection is made.

You can then escape to command mode at any time by using the
correct sequence.  By default, this is the three-character
string "+++".  Because this string could legitimately occur
within data being transmitted, some timing parameters need to
be correct as well.  The three "+" characters must be close
together in time, but separated from any other data by a pause
of a second or so (the "guard time").  You'd normally escape to
command mode prior to terminating the call with a hangup
command like "ATH" or "AT+CHUP".

To pass from command mode back to data transfer mode, the
command is

       ATO

(that's the letter "O", not the number zero).

John