Mine didn't sit and knit, but she did sit in the corner quite unobtrusively most of the time. I didn't want any backrubs or anything like that anyway, but DH was the one who was up and about by the bed, holding the gas and air, giving me a damp flannel etc...
The pre-prep meetings were really good, we debriefed the first birth and talked about hopes and fears (mine and DH) and made a rough plan and options.
What she did on the day was back me and DH up. At what point I wanted a cereal bar, but the MWs had said they strongly recommend no food. The doula said go ahead and eat. Where I think my DH might have said 'better do what the MW says'
And what she did was watch me so she knew how the labour was progressing. When the MWs pop in and out they have to rely on the monitor because they are not watching you continuously. But the monitor kept losing connection when ever I moved, so that would have meant staying sitting/lying on the bed. With the doula there I could take off the monitor and move around, because she could see if anything changed, where as DH (or me) would not have recognised how labour progresses, and spotted warning signs of problems.
At one point I remember the midwife coming in and saying save your energy love you've got a long way to go, and the doula said no you are nearly there (I thought you're just saying that because i'm paying you!
) - and when they examined me I was at 9cm.
The egg-timer protocols they have are there for safety, based on statistics and erring on the side of caution, based on you labouring without someone there monitoring you all the time. The doula being there is like an extra safety mechanism that buys you a bit more time and flexibility if you need it, rather than just going against the medical protocols without 1-to-1 care.
She also gave DH a chance to go to the cafe for a cuppa, and went and made toast after the birth.
I do think your DH is being unreasonable in not even agreeing to interview/meet a prospective doula or two.