ESP8266 (esp-07) powered by battery(s) for at least 1 year
If you are using ATTiny then you don't need to put ESP to sleep mode. You can disconnect power from it altogether using MOSFET or power management IC.

Now, ATTiny85 is not the best choice for low-power application. ATMega328P can run on button cell for a year.

Also the rechargeable lithium battery is really bad choice for this application too. You'd need voltage sensing circuit and cut-off to avoid damaging the battery. And if it is activated then you have no alarm at all. The better choice would be either alkaline or non-rechargeable lithium.

UPDATE

Finally, what's to stop hypothetical robbers from closing the window/door behind? If you only check once a minute there is a possibility that alarm won't be triggered at all.

Better option is to use NC reed switch. Then the voltage on the line can be used as wake up interrupt, so your MCU can sleep indefinitely, or wake up once a week (if you can find suitable ultra low power timer) to check battery voltage. I suspect with this setup battery can last for many years.

Furthermore, if you use timer chip with manual input you can connect your sensors to that input and connect power switch to timer output. Then you wouldn't need second MCU at all.