Remote control app for Android and iOS

Please do not bid any more than 100£ as it will be ignored - this is the budget and ignoring it means - you are wasting your and mine time both

Hi All, I need help to build a very simple app for remote control certain aspects of another phone via Bluetooth and Internet.

Core things which will be needed to figure out
- Background app refresh
- Bluetooth connection
- How to keep the app alive even with elongated periods of being in the background
- How to make sure the controls work even if another app is in the foreground and active
- Needs to be a simple and very little memory usage so that the device does not shut it down for want for memory
- will he likely 4-5 screens only
- Need one app for Google play store and one for apple - ideally a single app
- Will need a bit of design work as well - but the app is so simple that it should not be tough
- Will need to test the app and also host it on both my apple and android accounts

Here are the detailed specifications
https://docs.google.com/document/d/1-QOcsw_hJFHUshNF3aD-1HT94XmKzhsy06pt8Rubyns/edit