First and foremost, with proper love and support, I'd suggest that children are very good at dealing with change -- though of course they may prefer not to have to deal with such change.
At this point whether or not to divorce may be a choice but in an unhappy marriage things have a way of changing such that one party or the other will eventually force the divorce because they want out or in fact have found someone else that they want to be with and need the divorce to allow that. I'd suggest do the split up while it is easy for both of you to be amicable about it.
Also, once split, you may want to negotiate a period of delay before either of you introduce someone new to your children. Try to let them get past their concerns about the last challenge before throwing more at them. Basically, make their transition(s) as easy as possible. Keep in mind, a very large percentage of families go through this and there is not much stigma associated with it anymore.
The best advice I can give is make sure that the divorce, assuming it happens, is done in the most amicable way possible. For example, my own divorce consisted of a handwritten agreement between the two of us and cost us the court filing fees as we went there together and filled out the necessary paperwork. We discussed and agreed reasonably on everything possible.
For the children it's important to know, and be told from time to time, that both of the parents are going to continue to be around and that both parents will continue to love them very much. It's also vital that they don't imagine they had anything to do with it -- sometimes kids will imagine that they somehow caused something. So, they have to be told this explicitly as well.
As mentioned by @sbi, you must do your best never to talk badly about your ex or any family that the ex later becomes involved in. Children will pass this back and forth, even without meaning to, and even if they did somehow manage not to they may well feel conflicted due of their love and loyalty to both parents. However, it is certainly okay to let them know that no matter what happens that you will always be their father.
My daughter, the younger of my two children, would tell me that she wished we could still all be in one house or in the old house. It broke my heart. While I could agree that it would have been nice if things had worked out that way it wasn't possible. After a while I told her that it makes me sad to think about that -- so while she can feel that way I'd prefer if she didn't tell me so very often.
Some additional things to consider, many of which depend on age, are how close the two you may need to live in order to preserve daycare, schools or other attributes for the children. This may not be permanent but if you can minimize impact in other areas (such as new school, having to make new friends, going to a new day care, etc) it will help the children.
In a practical sense, you'll also have to teach the children to understand that different houses will have different rules. My ex and I keep very different schedules and we are very different with respect to the importance of timeliness. Surely a challenge as bed time and waking times change upon going from one home to another, but personally, I consider their ability to be flexible and adjust to different settings to be a valuable life skill.
You might also have to deal with your employer a bit. If your employer wants to be family friendly they will have to accept at least a variable schedule upon some type of shared custody. For example, in a week by week custody switch you can work tons of hours one week but lighter hours the next. Travel, if necessary, would hopefully be on weeks you don't have the children. I hope your employer will be understanding.
I'm not sure of the age of your children but I've answered in terms of the age of my own children through these events. As an important consideration, I'd suggest that both parents being happier (whether single or in new relationships) provides a much healthier example of how to live your life than demonstrating that life is about being unhappy until the children leave.
Also, a final note, work through your finances carefully. Having to maintain two households is more expensive than a common home. Whoever may end up paying child support will feel the pinch. Daycare and babysitting costs are likely to go up. You may find that more food spoils as you need to buy items for them before arrival that may not all be consumed while they are there.
While finding it financially challenging to split up may not be a reason to stay together you will both need to be realistic about what lifestyle you will have if you do so.
