I usually give it a week (unless I feel incredibly awful) or so to see if I can kick it, and then I start thinking about the IVs. I usually know whether it's a cough too deep and strong for me to kick myself or if it's a job for IVs. Basically, once I realize I'm in a situation that I can't get out of myself, I accept what needs to happen so that I can get better as soon as possible.
As far as the kids, I'm not sure, but do you have any family that could help during this time if Mark needs to go in? I think he would probably need to go in to the hospital to get the IVs started so they can make sure the levels are okay and the meds are the rights ones, no side effects, etc, etc.
Eventhough your veins are probably pretty strong since you haven't had IVs before, the IV meds can be very harsh on veins. Because of that, the midline (regular IV lines) can blow in a day or two after they go in, leading to more pokes then needed.
I hope you get over this crummy cough soon! Let us know how it all goes.