I wouldn't count on the flight staff allowing you to wear her during your flight. We flew with my baby a few months ago, and when I boarded the plane I was wearing my baby. The flight attendant told me upon entry into the plane, "Just so you know, the baby has to come out of that when the plane is in motion." (which I already knew)
We have flown with all of my kids while they were babies, and to give my arms a rest while they slept, I simply folded down the tray table & rested my arms on it. It helps a LOT.
Honestly, I don't think that you will need your husband's help if you just plan to be as hands-free as possible:
Check your carseat
Check your large luggage (Southwest gives you 2 free)
Wear your baby while walking through the airport (although you will have to take her out at security & just carry her--do this LAST, after you've put through your carry-on & liquids (if applicable).)
Use a backpack for your carry-on.
Make sure you are wearing something with good pockets to put your ID & boarding pass in
Edited to Add;
Yes, you can gate check BOTH the carseat and the umbrella stroller.