If you have JOINT legal custody, he has as much right to get her immunized as you do to opt out. If the two of you can't agree on this medical issue, and there's no "tie breaker" provision in your custody order, you'll likely have to head to court and let a judge decide this particular issue.
If you have SOLE legal custody, that's another issue all together. In that case, he wouldn't have the right to make medical decisions for your daughter one way or the other. If that is at issue, the legal ramification wouldn't be for trying to give shots to a child with the exemption, but for violating a custody order which denies him medical decision making power. He could be fined and you could move to have other aspects of your custody order modified moving forward.
If your issue is that YOU (either individually or collectively at some point in the past) decided to exempt your children from immunizations, and he wants to violate that decision, you can't really use THAT as the your argument. Parents make and unmake decisions all the time throughout their children's lives as they gather new information, experience, and perspective. An immunization exemption is a documented choice, but it isn't a binding, lifelong commitment, and it certainly doesn't EXCLUDE your child from access to immunizations for all eternity.
Talk to your daughters father. Really talk... listen... and try to agree. If that fails, you'll need to file a motion with the court to try and get sole medical decision making authority (at least on this particular issue). But be forewarned when you file... you're likely NOT to win this legally, so be prepared that if you open that door, you may not be able to close it later.
Hope this helps,
T.