What is "a mother's day out"? Are you sure they will ask about vaccinations? I wouldn't fill out the form falsely. At the end of the day, it's their policy, and you should respect that.
What kind of exemptions does your state have? I would make sure I have that letter/signature/whatever on hand, just in case. But they may not even ask for that kind of thing.
They won't ask for her vaccination record.
At most, they might ask if she is vaccinated, and then you could say yes. But they probably won't even do that. And they definitely won't ask for proof.
I wouldn't falsify anything. Chances are they won't ask, but there must be a database somewhere (at least in our state) because our private school was able to look up our records. I doubt your personal records would qualify as proof anyway. If there were a requirement, it would probably be in the form of something with a MD signature.
A good reason to be honest is for the protection of your own child. If pertussis (say) is going around, you want to be notified so that you can keep your child home.
If there is disease exposure in a childcare or school setting, every parent is notified. Not just parents of unvaccinated kids.
Also, a mother's day out program would not have access to a state vaccination database, unless they are part of a licensed childcare center. But that is a good reminder to get yourself removed from the database.
Depending on how official the program is, they might not require vaccines/exemption forms. But it's official enough to need them, it's too official to give them fraudulant info. In Texas you need to request a form and fill it out - they allow religious and philosophical exemptions but make you jump through some hoops for it. Here is the info:
From my experience with working in and now sending my children to daycares, the staff cares more about being compliant with their licensing rather than if your kid has been vaccinated. So, if they require something, turn in an exemption form. Good luck!!!