No need for the second appraisal, but the first one is a good idea. If you both want to save money, many real estate agents will also do a similar valuation for less money.

The point here is that at the point you divorce your house will be worth a certain amount and you'll owe a certain amount. The difference will be the equity. That amount needs to be split between you, 50/50 is usually the right ratio unless there is a serious reason not to. A good example of this type of reason would be for one of you to have depleted your life savings to make the down payment while the other one didn't contribute anything.

Once you're divorced, the house and equity isn't yours anymore. She's making all the payments, so she should get all the equity. Unless you have to repo it from her due to lack of her keeping up on the payments. So forget about a second appraisal. By getting divorced and letting her have the house you need to give up on any future benefits from it so don't tie any payments to the value of the house.

Instead any payment from her to you needs to be compensation for you tying up your available credit and taking on the risk that she will end up trashing your credit. Think of what a single missed payment will mean to your credit score. The fact that she can't afford the payment after a refinance indicates that this might be too much house for her, and she runs a high risk of default. I'd think somewhere in the range of $0 for the first few months, then add a figure such that she's paying about 1/4 what she's saving by not refinancing for the next year, than 1/2 then 3/4 then 1, then 1.25 and so on. (So if her payment would go up by $400 by refinancing, it would be $100 for the first year, $200 for the second, and so on).

You might also want to consider some sort of escrow account that is structured in a way that neither of you could withdraw money from it and which has a couple months of house payment in it. She'd make her payments to this account and The autopay on the loan would come from this account. You could monitor it to make sure a payment is not missed and if it is, it gives you a month or two to fix before a payment is missed.

One thing she needs to be aware of is that I don't know anyone who expects interest rates to go down in the near future. The fed continues to raise them fairly aggressively to try to get inflation under control. No one knows for sure but it wouldn't surprise me if the rates don't get lower than they are right now for at least a couple if not a few years.