Yes ... each home can be reported separately  BUT ONLY IF  you did not use the joint exclusion on the 2020 return.  If you only used your 1/2 of the exclusion on the 2020 return then she still has her 1/2 of the exclusion to use on the 2021 return.  

For the "2 years of the last 5 years" rule, "ownership" is imparted by marriage but not residency. 

You can file a joint return for 2021, but the maximum exclusion your spouse can claim on her home is $250,000. You can't use the full $500,000 exclusion for 2 reasons:

1. you used your own exclusion less than 2 years before your spouse sold her home,

2. you have not (I assume) lived in your spouse's home as your main residence for 2 years before the sale date.

Then, you can't use the full $500,000 exclusion for the sale of another home (if you need to move again) until 2 years + 1 day after your wife used her exclusion for the 2021 sale. 

It doesn't matter if you file joint or separate. You already used your exclusion on your 2020 tax return. Therefore you can't take the exclusion again for 2 years after the closing date of your house.

If your spouse sold their house in 2021, then your spouse can use her exclusion on the sale of their house. But you can't take the exclusion on the sale of their house for two reasons.

1) you took your exclusion on your 2020 tax return.

2) You did not live in the house (I assume) as your primary residence for at least 2 of the last five years you/they owned it, counting back from the 2021 closing date of the sale.