You don't say where you're at, but no doubt different cultures view this kind of thing very differently. Here in the US, dating outside religion, race, is much more accepted than say in a middle eastern or asian country.
If that's the way life is for you, where you're at, it's going to be difficult for you, as your family likely won't budge on the issue. Not that I'm one to encourage a person to cave into what others want, but at this point, if you're only dating, can you NOT date a Muslim man? Are you a practicing Muslim yourself? How long have you been dating this latest man? It sounds like on top of the issue with religion, it's a big no no to go away with a man (maybe before you're married)? It sounds like you're going "against the grain" on a lot of issues that are making life difficult for you.
Unfortunately, if this is a cultural thing, YOU are not going to change everyone. That would mean you have some decisions to make, and decide if it's worth all of the stress and basically being disowned because of who you date. Or, if it may be easier (and better) for you to try to FIND a Muslim man (especially if you're active in the Muslim faith) who you can be with. Do you prefer Christian men, and if so, why? Is there a difference in how they treat you? I wish it were as simple as saying "you be with whoever you want, who CARES what people think", but I know in some places in the world, that can be a dangerous prospect.
I'm sorry for the situation you're in...always keep in mind that whatever decision you make, there are children involved that have to face any consequences along WITH you that YOU have to deal with, sadly.
Best to you.
It's YOUR life, not your family's. If you like Christian men, then date them. You can still worship in your own way. Another name for that is FREEDOM OF RELIGION. I find it silly how some religions shun others. Everyone who has a religion is praying to the same thing, no matter what name you want to give it. I hope you find your way, as I'm sure you will. I'm done putting in my two-cents. :-) Blessings - Blu