Okay I'm going to give a different answer. See I am married, have kids, and yes a boyfriend. He was brought up very mono and very religious actually. His strong faith is part of what I love about him even though we do not share the same beliefs on everything.
He has had to do a lot of questioning and asking about us and about himself to see if this was something he could do. Much of that is internal work. Though don't get too worried. Hubby and I had to do a lot of internal work before all this too! Being strong in yourself and each relationship is important.
It can work out yes. Long term is what we want, and though it means it will be a different relationship than the one hubby and I have, it won't be less. I'm not expecting or looking for a brother husbands thing. Or a threesome, as both my men are straight! So no there will be no bed sharing, but I don't rule out living near each other, having intertwined lives. I don't expect bf to start acting like another parent to my kids. He has talked with them, and we don't label things. They call him by his name, he has nicknames for all of them. He sends them things he knows they are interested in and they share their good news with him as well. You could say it's like he's an uncle but again, we don't label and they know he is a love in my life, they are all pre teen and teen however, and have grown up around lots of different kinds of families so are okay not labeling things.
That will probably be the hardest part. We as people like labels. They tell us what to expect. Having a relationship that has no label or no label you are familiar with takes some getting used to. Don't be afraid to ask if you need reassurances. If you need to talk it out a lot. With her, with both of them. Take it slow, be honest and you should be fine!
Me: Late 30s pansexual poly. DH: My husband of 17 yrs and father of children. DC: LDR of +2 year