Much of what I read here is spoken in ignorance or just blindly and plainly attempting to defend homosexuality or erroneously making assumptions of what my daughter's response would be and/or totally ignorant of how aggressive the LGtb community is targeting Christian business owners.
Fact is: what I have stated about the LGtb group is in fact occurring. They have strategies in place to trap Christian business owners. There is no way they will engage a Christian without a prepared dialog to force the issue and get a statement from the business owner regarding their position relative to their sinful lifestyle. Whether a business owner is a Christian or not can be or should be quickly discerned from a quick search of their web site. Throughout the Bible we are admonished to take a stand for Christ, be courageous, be separate from and expose evil, and be not ashamed. In fact, in Rev 21, I believe, the cowardly are grouped with unbelievers, murderers, sexually immoral, and liars. So, if they ask, which they will, are you saying to lie or not take a stand/be a coward?
It depends on the laws of the state of Michigan, and of the City of Muskegon. The State of Michigan does not at present, to my knowledge, have anti-discrimination laws that would override the inherent right of business owners to decide whom they serve (as long as they don't violate federal antidiscrimination laws), but the City of Muskegon has included LGBT in their anti-discrimination statutes, so it is likely that were she to refuse to provide her services on the basis of a couple's LGBT status, that the couple could bring a discrimination lawsuit in the city courts of Muskegon and prevail.
So, your daughter has a few options here:
(1) If she wants to become a test case and carry a formal legal challenge to the LGBT forward, she can violate the Muskegon ordinance, take the legal hits (which will probably include being shut down, at least temporarily, and losing in the local courts and being ordered to pay hefty fines and damages to the gay couple), and then appeal the decision on constitutional grounds. To have a hope of winning she will have to have good legal counsel. Perhaps she can prepare a trap of her own by consulting with religious rights lawyers BEFORE she takes the stand, so that she refuses service in a way and using the words that are specifically designed to give her the most favorable case in a lawsuit.
If she affiliates with the right religious liberty defense lawyers, they may partially fund her legal efforts or even do it pro-bono.
However, she should be prepared to lose and to spend a great deal on the legal effort, thereby becoming a martyr. She should not expect to find too many lawyers willing to join her in economic martyrdom.
The Supreme Court case that Redleghunter mentioned may cast light on this.
(2) She can knuckle under to the law, and think in terms of the segregationists who truly believed, in their heart of hearts, that blacks bore the mark of Ham, and that it was genuinely evil for the races to mix. There were people who sincerely held their segregationist beliefs on religious people. American law made no allowance for them, and when they were discovered they were rooted out and all driven out of business. Or they swallowed their religious beliefs and decided that they needed to stay in business, and bowed to the superior force of law even if they did not change their minds.
As a practical matter, this makes the most sense, and is a long-standing tradition among Christians going all the way back to Jesus' admonition to the Jews to pay taxes to Caesar EVEN THOUGH Caesar did things that were an abomination to Jews and before God. God will enforce his law.
Jesus said that his followers would need to be many things, but one of them was "wise as serpents". Serpents are known throughout the Bible for their sneakiness. Essentially, faced with overwhelming force, the Christian can chose to be a martyr, or he can choose to follow Jesus' advice, pay the taxes, be a serpent, and wait for the day when people have had enough of the evil, then rise up politically to throw off the bad law.
As long as she provides the services, nothing legally prevents her from being politically active in efforts to overturn the law. There may be business consequences to that, but those would come in the form of a boycott - which would obviate her need to serve LGBT.
(3) She can move elsewhere, where there are not such laws.
There are variations on the theme, but essentially her choice is to fight, almost certainly lose the opening battles, and perhaps maybe win in court in the end, or perhaps be a martyr and have her business and assets stripped from her by the law, or she can bend the knee to the law and resist it mentally and perhaps politically, or she can clear out and go someplace where she will be legally protected, or very unlikely to face the problem.
Those are the choices. Possible victory (but probable martyrdom), serpenthood, or refugee.
I will add that I believe the best answer is serpenthood. She has a young family and she needs to succeed. That means that she has to compromise with the society in which she lives. To pay taxes to the Romans MEANT that the Jews were actively providing the means for their oppressors to remain there, enforce their laws...and ultimately pay for the Army that destroyed the Temple itself. Jesus knew that. He told them to pay their taxes anyway, the alternative being an immediate revolt against the Romans which, Jesus knew, the Romans would win with great loss of life to the Jews. So, even though people could logically argue that paying taxes to a warlike and murderous state is "support" for the war and murder and torture and all of that that warlike and murderous states do, Jesus cleared people of that potential guilt: he told them to pay their taxes anyway, not to throw away their lives in a hopeless fight against a superior foe, when God had given no sign or promise of victory.
The advice I would give is to be a serpent and not turn away LGBT if they come in to get the pictures done. Because all of the alternatives amount to economic martyrdom and professional suicide, at great cost to a young family.
Knuckle under and recognize that God sees your oppression and knows who your oppressors are, and is just.
