I don't think either of us would be too happy if I just forced the baby on him for a couple of hours. The baby doesn't sit with him calmly for very long, maybe half an hour tops. After that, he needs me to calm him down.
And how will Dad get BETTER at baby soothing unless he practices and clocks the time? How will BABY learn Dad can also soothe baby unless he practices and clocks the time? The role of the father is to teach baby comfort can come from OTHER places too -- not just the food lady.
And how will either DO this learning, if Mama won't just surrender baby to Daddy and walk out of the room? Because Mama herself needs to grow her confidence in Daddy being able to handle Baby and she's not gonna unless she gives the baby up to Daddy sometimes and just let's them figure each other out and get all kerfuffle. You have to stretch and sometimes be a bit uncomfy to grow.
Not leave the house -- just leave the room. Give him baby all nicely topped up from nursing and check out to read a magazine, do internet fun, catch a movie for an hour. Refill the kid, then hand him back to dad. You don't have to pump if you don't want to. You have to surrender NON NURSING ACTIVITY to regain your mental health balance.
If your are at the 30 min tops place? Go get your 30 min. Grow it to 35 min! One baby step at a time, eventually you grow it to longer and hallelujah! You get to the place where you can leave the house for a few hours.
You are the SAHM and clock way more baby hours daily - so YOUR baby skills grow at much faster speed and baby's trust in you grows that much faster. That is natural and normal.
But don't let Daddy off the hook just because he's clocking baby time at a slower time. He's a parent too -- and that means YOU have to suck it up a bit on watching/listening them figure each other out even if you have to leave the room. You do your baby and Daddy no good in stunting their rship development time, and you do your OWN health no good by not taking the break.
Did you have this baby together or not?
I understand some things you cannot do or help because of finances imposing limitations. But this one? There's no limitation there you cannot just change. Today. Tomorrow. Get on it. Fix the ones you CAN improve.
You have been thru my suggestions and other people's and explaining why not so or not yet.
How about making a post listing CAN DO NOWS then? To help your mindset? And sort some of those others into piles of "DO THIS YEAR" and "DO NEXT YEAR" or whenever the time break out is. Then you can feel better knowing some things WILL come down the pipeline for you. Like NOW, medium and longer out things for yourself.