No you cannot have two routers connected.
As you are having power installed to the shed, now would be an ideal time to have some Cat5e or Cat6 cable laid too. Not in the same duct as power but can be in the same trench. Have 2 x Cat5e/6 SWA (Armoured) cables laid between house and shed, and terminate with RJ45 wall mount sockets. The second is a back up in case of failure- albeit unlikely.
Install the modem/router where the phone terminates and connect a patch lead from the router to an RJ45 socket, then in the shed a similar patch lead to a small 8 port Gbit switch.
There are other potential options with two cables running between the locations such as modem at house, router in shed, then a feed back to a switch in the house for example.
M H C
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