Is the funeral really going to take half an hour or less? You said you want to drop your baby off at 2.50, go to the funeral and be back to collect her at 3.30 - have I misunderstood? I've been to a few funerals recently, mostly basic cremations, not even full church services, and none has been that short. Usually you'd expect to get there 10-15 mins beforehand, the service is maybe half an hour, then everyone is outside for another 15 mins or so to offer condolences, look at the flowers, etc & I think it would be really rude to leave straight away, especially for close family. And why aren't you going to the wake? I think YANBU in expecting your family to help out at a time of need, but also I wonder if your family think it will actually be a much longer amount of time than you are saying?
I also agree with everyone saying to take your baby with you. Taking older children is different, that's a decision you need to take depending on your own children and how they might cope, but it's surely ok to take a baby to a funeral - as others say, stay at the back and you can step outside if your baby is crying. If your dh's family is really likely to start fighting, maybe having a baby around will help calm them a bit.
Another idea, rather than ask a friend to take time off work which they might feel awkward refusing, could you put something on your facebook to ask if any of your local friends could possibly mind her for an hour or so during the funeral? That way someone could volunteer if they can but don't have to feel bad about saying no. And if your family are on your fb, hopefully they might feel guilty.