No.   If you are divorced even as of December 31, 2021 you cannot file a joint return for 2021.  Your filing choices will be Single, or for the custodial parent--Head of Household,

Am I Head of Household?

https://ttlc.intuit.com/questions/1894553-do-i-qualify-for-head-of-household

https://ttlc.intuit.com/questions/2900097-what-is-a-qualifying-person-for-head-of-household

If you qualify as Head of Household, when you enter your filing status (single or married filing separately) into MyInfo, and then enter your qualifying dependent, TurboTax will offer HOH as your filing status.

If you are not legally married as of 12/31/2021 then you can only file your tax return as either Single or Head of Household.

See this TurboTax support FAQ for Head of Household filing status - https://ttlc.intuit.com/community/family/help/do-i-qualify-for-head-of-household/01/25539

no you can not file a joint return with your ex. to file a joint return you must be legally married at 11:59:59pm on 12/31/2021

the tax laws may not follow the divorce decree as to claiming the children as dependents. it's the tax laws that control.

to qualify as head of household a taxpayer must meet all of these tests. IRC Sec 2(b)

1) the taxpayer is not married at the end of the year

2) the taxpayer paid more than 1/2 the cost of keeping up his/her home

3) the home was the principal residence for more than 1/2 the year of either of the following:

= the taxpayer's qualifying child 

= the taxpayer's qualifying relative who is the taxpayer's dependent with certain exceptions

4) the taxpayer is a US citizen or resident during the year.

not meeting all these tests means that an unmarried taxpayer can only use the single filing status

the custodial parent is the one that can claim the qualifying children as dependents unless that parent furnishes the non-custodial parent with form 8332.

if the divorce decree grants the non-custodial parent the right to claim the qualifying children as dependents, failure by the custodial parent to comply could result in that parent being held in contempt of court.

Your custody and dependent situation becomes very important here, and is sometimes even more tricky to figure out in the year you divorce.  You will want to read publication 501 and 504.

https://www.irs.gov/pub/irs-pdf/p501.pdf

https://www.irs.gov/pub/irs-pdf/p504.pdf

Very briefly, the parent who the children actually lived with more than half the nights of the year is the parent who can automatically claim the child or children as dependents.  Most of the time, the child can't live more than half the year with both parents.  However, in the year you split, it can be possible for a child to live more than half the nights of the year with both parents.  For example, if you separated on March 1, then the children lived 60 nights with both parents.  If you then shared custody 50/50 after that, then both parents get "credit" for 210 nights of custody, and both parents have the right to claim the child as a dependent because 210 is more than 183.  If you agree, you can split the children any way you like, and neither parent needs a form 8332.  If you can't agree, the first tiebreaker is which parent the child lived with more nights (even 1 day difference, like 210 days vs 209 days).  If it is exactly the same number of nights, the second tiebreaker is which parent has the higher taxable income.

In future years, this becomes easier to figure out because its generally impossible for each parent to have custody exactly half the nights of the year since there is a odd number of nights; only one parent can have actual physical custody more than half the nights of the year.