OP I have some really bad news for you....
- If you have a morale problem in your team then you need a mirror - not a "team event" - they do not solve team morale. People don't leave jobs or teams - they leave managers - ie you.
- 99.99999% of people HATE "team events" - I cannot believe that companies haven't "got" this yet and still try to force this crap on their employees under the dubious guise of "fun" - they're crap and everyone knows they are crap. All they do is take people away from the (excessive) work they're trying to get through to meet their invariably unrealistic targets!
- From your corporate BS posts alone I know EXACTLY what the "culture" is your company without attending your cringy team event! I suspect your employee knows too - which is why she doesn't want to give up her own valuable time to attend your BS event.
Honestly - it baffles me that you think your corporate "party line" tripe is fooling anyone. Everyone sees straight through it; it's BS and everyone knows it. "We care about our employees' well-being" is the biggest lie in the corporate world these days... usually said while employees are being discriminated against, bullied and bombarded with workloads and environments that are designed to make them crumble. Then when the employee tries to set a boundary for their own health, it gets chipped away at while all the time criticising the employee for "not being a team player". No - they simply haven't drank the corporate Kool-Aid and are prioritising their LIFE.
I used to be that person - going the extra mile (many extra miles in fact!) - but the simple fact is, that "extra mile" only ever goes in one direction! It's corporate BS speak for making your employees work for free.
In this particular situation, your employee agreed to work on a Tuesday when required for project delivery; in other words - when it's urgent and essential in order to meet a project deadline. It should be the exception - not the norm.
A team building type event is NOT urgent or essential to meet a project deadline and in fact, all it does is put employees back in terms of their workload so they end up more stressed because they've missed out on a day when they could and should have been getting actual work done. Your employee of course will not be happy with taking a different day off because, rightly so, she probably wants to use that day for her ACTUAL JOB - not some bullshit event that wastes time, money and just annoys everyone while work is backing up.
If you consider your ridiculous team event (that no one wants to go to btw! You do know that right?! Please tell me you're not THAT delusional!) to be so important - schedule it on a day when your employee is being paid to be there and don't expect her to rearrange her personal life for it.
Finally - be very careful about your attitude towards your employees; treating people less favourably on these types of grounds is tribunal territory.