I think the other answers missed the point of the question.
It sounds like you want to sell house #2 in 2022. House #2 is jointly owned and lived in for more than 2 years, but you used your personal $250,000 exclusion less than 2 years ago on house #1.
I believe the answer is yes: if you and your spouse file separately in 2022, your spouse can use their individual $250,000 exclusion. However, there are a number of potential issues with this.
First, if you are in a community property state, each of you must report half the sale and half the gain. You will pay tax on your half even if your spouse uses their exclusion on their half. Even if you are not in a community property state, you should probably each report half the sale and half the gain, but I can’t cite a regulation one way or the other.
Second, filing MFS could negatively impact many other tax provisions such as IRA contributions and the child care credit just for starts. When filing MFS, if one spouse itemized deductions on schedule A then both spouses must itemize even if the itemized deductions are zero. You can’t stack the itemized deductions on one spouse and have the other spouse take the standard deduction.
Regarding amending your prior tax return, if your gain on the current home is larger than the gain you excluded in 2020 on home #1, you could file an amended 2020 return to pay tax on the gain, then you could file jointly in 2022 and claim the full exclusion on the sale of home #2. It would not be necessary to change your filing status on your amended 2020 return, you still file jointly but list the home sale and pay the capital gains tax.
