I'm detecting a possible lack of respect for him here, the way she's arbitrarily rejecting all possible contraceptive options except vasectomy and refusing to listen to his concerns
I agree.
In the nicest possible way OP, it comes across like you're a bit of a pushover and your wife is dominating.
You sound defeated when you say you'll probably end up getting a vasectomy as it's the only way.
She's taking away your ability to father more children, while firmly keeping her ability to have more children in the future.
If she was dead set against ever having another child and so very fearful of using condoms, then she would get sterilised.
It sounds like it's her way or the highway.
Nobody gets married expecting to divorce...but I believe almost 50% of marriages end up in divorce.
If you were older, then it would be fine.... but 30 is young to make this permanent decision.
You've already said you feel like you compromise more and put more effort into the relationship.
Even the way she said she'd pay to freeze your sperm...well you're a SAHP... so it's not her money it's family money. You can bet your bottom dollar that would be spouted out if a man said what she did. She's saying it like she's doing you a favour.
She holds all the power in this marriage. Usually it's a case of he who cares the least in a relationship,
holds the most power
I don't know what your day to day life and routine is, but I would encourage you to look after yourself physically and mentally. Go to the gym or do other exercise.
Have a social life outside of your family/ marriage...develop some personal interests. Think about what you'll do when the kids start school.
You're more than a husband and a dad. Do things you like and enjoy...just for you. Don't isolate yourself and if you've drifted from your parents/siblings, keep close links.
Consider training for a new career...do some volunteering.......do not let it be that your wife is the centre of your universe, or you will really struggle if things go wrong. You sound quite passive and I think she knows by digging her heels in.... you'll cave.
Situations of full financial dependency on a spouse leave you in a vulnerable situation and give rise to contempt and resentment.
I honestly think you need to allow yourself time to think and possibly explore your feelings with an independent professional like a therapist. Not couples counselling...just you.
I'm sure much more than the V will come to light about your relationship and really bring up things you've overlooked....or know deep down and accept, so as not to rock the boat.
There are non hormonal options, but she has outright refused them. A cap and a condom combined would sort this out...I would never pressure my DH to undergo any form of surgery.
There's little to no regard for you and your feelings from her.