Usually it gets easier, little by little. But all relationships are different, and you can't always guarantee that a particular relationship will "stick for the long haul." It sounds like you have some trust issues where DI is concerned. That's quite a large problem, and you'll need to find a way to get past it eventually, if things are going to succeed. Do you and DI ever get out and do things just the two of you? or is that part of the relationships just too tension-filled for any kind of friendly get-togethers?
It may get harder before it gets easier, but it should get easier eventually. Just try to look at the situation from as many angles as you can.
Love means never having to say, "Put down that meat cleaver!"