I can't answer your actual question. but can only give you my impressions.
first It would take a long time for me to be comfortable with a stranger, unless they just had the spot on perfect personality. I don't like people in my home. so this would be a last resort for me.
I also don't really trust strangers with my babies so I have some issuse of my own.lol.
I guess, i also think, it would be rough and no you would not be the very best mommy to the 4 yo but you could do this all yourself if you were willing to sacrifice. that might mean letting dd watch tv snuggled w you on the couch while the baby sleeps in a pack n plan 2 ft away.
it seems a shame that your dh can't cut out a job and alter your life style so that you can be a family together, you would only really need the help for a year or so.
I didn't go research any past questions but i wonder why your dd would go to preschool full time.
am i being really slow? you work full time??, and hubs has 2 jobs and some of that money goes to full time day care, plus you are considering paying for night time help, is that a clearer picture? but what is the day time post partum doula for? gah sorry i'm confused.
i guess either of those options work, cutting back work hours would work, hiring a college or high school student in the afternoons to playgames and entetain the 4 you might work -- personally i would find that less threatening if it was a highschooler who was earning childcare experience while i was physically present, waiting until dd is in kinder might be another option too.
good luck and please clarify what ever it is that im missing.
edited: I"m so sorry sweetie, but i just am not ok with this question. probably some life experience of my own that i am projecting on to you but something is just off and i feel like i need to tell you that bringing another life into this world with daddy not around and mommy not being present for what ever reason, just seems awful to me. another baby will add more stress to what ever is going on. I don't think it's a good idea. again sorry. just my opinion but i would advise being happy with your one child.