Tan- Izzy is sounding just like how Ashleigh used to be. I went thru all that an and off for months, tried everything, eventually she just started doing it. It wasn't til she was bout 9 months though, hopefully you'll get success sooner.

As mentioned try going out for 6 hours and see how she goes. She may surprise you. If she is on solids maybe slip in a little extra while you're not there if she is refusing the milk.
And the cup might be good idea or you could even try a syringe? Just to get what you need into her while not there.

Good luck with it all, I totally understand how you feel, I used to feel trapped at times, there'd be times when I just needed time out but was so hard cause Ash was feeding like 2.5 hourly up til 6 months.