You should try the modem plugged in directly on the pc. DECT phones use other frequency bands and if your DECT is OFCOM certified (not sure if they do certify wireless devices like ICASA in SA) then it "shouldn't" be interfering in other bands.
I just think the DECT phone is preventing the 3G modem from going from the unplugged state to the identifying state. I think the ZTE MF112 3G modem might have some sort of compatibility issue with the Router although the firmware supports it. If I could find a modem bin file for the MF112 maybe I could try that. In anycase since the DECT phone has been hung up I have not had to reboot the router to get the Internet going again.
EDIT: Not entirely sure I am giving it enough time to go from unplugged to identifying as now when I lose the connection, sometimes it does say unplugged but then switches to identifying and reconnects to the Internet. When I woke up this morning it was in the unplugged state and did not seem to want to recover but maybe I am not giving it enough time to recover.
EDIT2: It seems that as long as you have the 3G stick set to connect on demand when it loses the connection it will go from unplugged to identifying and reconnect to the Internet automatically, however whilst the DECT phone was in use it did reconnect but the Internet was unusable as I could not ping any sites, had to manually disconnect and it manually reconnect again which I happened to do when the DECT phone had been hung up then it worked fine until I lost the connection again some time later but it automatically reconnected OK. So it appears the DECT phone does have some impact of the functioning of the router *sometimes* and I recommend you have it set to connect on demand with an idle time of 15 minutes.
EDIT3: I disconnected and reconnected whilst the DECT phone was in use and the Internet worked fine, so it appears that the DECT phone does not always have an impact on the functioning of the router OR that sometimes when the router connects you cannot ping any sites without reconnecting but as long as you have the modem set to connect on demand it will always go from unplugged to identifying and then connect to the Internet.
EDIT4: It appears that when the situation arises that it connects to the Internet but you cannot get to any sites or ping any sites then it is time to reboot the router rather then manually disconnect and reconnect as although that might work the router is on its way to crashing and sometimes you cannot bring up the web interface after even. As I say this only happened the first time whilst the DECT phone was in use but that may have been a coincedence.
So to summarise leave the 3G modem set to connect on demand this means that when it loses its connection instead of just sitting there saying device unplugged it will reidentify the modem and reconnect automatically. However if you find that it connects but you cannot get to any sites a router reboot is the best option. As I say this only happened to me after a few hours and whilst the DECT phone was in use but its entirely possible that the DECT phone has no influence over this and it was just a coincedence. I hope this does not happen too much.
EDIT5: Right I have now managed to reproduce the problem where the modem stays in the unplugged state, it seems that when it connects but you cannot get to any sites or ping any sites the router needs to be rebooted and the modem needs to be unplugged and replugged.
When I only rebooted the router it connected but still no sites were accessible until rebooted it again and I unplugged and replugged the modem. It seems connect on demand does not work in this situation but it does work for the sporadic disconnects that you get every so often which can be recovered from.
Its just once it connects but you cannot access the Internet its totally screwed and the router and modem need rebooting and unplugging replugging and this happens from time to time and its nothing to do with the DECT phone.
It would seem that it would be a good idea to set the idle time to 0 so it remains active but regardless of this it will still lose the connection from time to time and sometimes its not recoverable without rebooting the router and unplugging/replugging the modem which is a shame. Most probably some incompatibility between the router and the modem.