What do you think your partner would do if you left him alone with the baby for an hour and the baby woke up? Would he step up, pick up baby, and try and see what he needs, or would he be straight on the phone to you expecting you to come back? I think I might be tempted to give this a try, as if baby sleeps right through, then you've had a chance to just escape for a little while, and if not, and your partner rings, just ignore the phone, then head home and see how he's coped. I think it may just be that like a lot of first time fathers, he feels a bit intimidated because you seem to know how to do everything perfectly, so perhaps being left to cope, might give him the confidence to at least try and do what needs to be done. You don't need to be far away, maybe pop to see a friend for a coffee, or arrange to have your hair done, at least then if he rings you can say 'I can't come yet', and give him instructions on what he needs to do, but you do need to force his hand a bit in my opinion, as otherwise, as you've already said, you will resent your baby because you will feel he has stolen your life.
Also, have you actually talked to your partner about the fact that you feel trapped because he's so useless? If not, then you need to, NOW!