I do know people can change their finances. Many on this forum are good examples.
You should let him make the change himself and pay it himself. However, since you are the more financial savvy I think you should maybe look into getting a Line of Credit, preferably an unsecured LoC just for him but maybe even a HELOC. If your mortgage is almost paid you should be easily able to do this.
I am not sure how you get the 60K total at 16.5% unless there are a bunch of hidden signing fees, or maybe he was underwater on a trade-in.
Please share your real math details and we will try to help.
I am assuming, and rounding, a few numbers here:
CURRENT SCENARIO: 30K 16.5% 5y = $738/month = $44280 total = $14280 interest
BETTER INTEREST SCENARIO: 30K 6% 5y = $580/month = $34080 total = $4080 interest
Get that bank LoC and save yourself $10,000
LOWER TERM SCENARIO: Even better, keep the payment high and lower the term to 4y
30K 6% 4y = $705/month = $33840 = $3840 interest
If he can make a $1000 payment that will cut the loan to 2.7 years.
30K 6% 2.7y = $1000/month = $32400 = $2400 interest
If you can save him, and your family, over $10,000 why wouldn't you?
It is completely foolish to punish him by taking care of this debt, at a horrible rate, all on his own. The "Your problem you deal with it" attitude is not good for a marriage. I don't think you should pay it, but you two sound solid enough that you can co-sign or help transfer his debt to a better rate. Talk to him about it. "I think we can save $10,000 if we do this... I still want you to pay for it but I want to help find the best way to help you get rid of this debt as easy as possible. After the debt is gone in x years what long term goal should we focus on? (Vacation, college fund, house reno, FIRE etc.)." Maybe sign a little deal on paper between you two that even though the debt is now in both of your names it is his responsibility. Even better, if you can just educate him enough to get his own LoC in his name. Let him shop around at the banks, he should be able to find a better deal then he will no longer be so "ashamed" about this financial mistake. In a few years he can say "I once had this horrible car loan, 16.5%, but I found a better deal of xx% and saved myself thousands."
How do you share day to day expenses? 50:50? Are you making advanced payments on the house mortgage? Who makes more? Is he accumulating consumer debt on toys? The eating out daily is a real problem for a families' finances. Eating out constantly also doesn't sound like a great trait for a SAHP. What is the kid going to eat, fast food every day? I try to impose an eat out cash allowance only rule on myself. Date nights together are different. Does he realize he could probably pay the truck off twice as fast, and save thousands, if he ate out only once a week?
More baby talk, first congrats on being "over the moon" IVF is a big financial and emotional commitment.
As for child care, as others have mentioned, daycare is not the end of the world for baby.
Both my SO and I are highly educated, and good with kids, but we gladly send the little one to daycare for just under 8h per day. All this week they are doing a mini Olympics with a field trip to a local gymnastics club. Stuff I just couldn't do by myself. I do feel sorry for the kids there for 10-11 hours. But with the right schedule with your TWO jobs daycare is probably the best financial decision. Once your mom moves she can pick the child up even earlier or have one day a week be Grandma day. Asking grand parents to look after children full time is quite onerous unless it is really the only cultural option. Visit a few Daycares, some will make you want to run crying, but others will make you smile and feel good about the opportunities.
And I know it is far from your mind, but the comment above about the SAHP getting custody, child support and alimony would be a true concern if you are not 50:50 parents and roughly 50:50 earners.