Please, explain a bit more here.To keep your domestic phone system working you will need some form or battery backup, but as such a simple router will probably only pull maybe 15W or so usually at 12V. Ergo such would pull about 1.5Ah from a backup battery, so 7 days cover would need around 10Ah.
I presume you are implying just peak values as the basic arithmetic of 1.5Ah equates to a lot more than 10Ah per week, ie that being 24 x 7 =168 hours?