I struggled with this too.
Quitting birth control was an absolute necessity for me, and as difficult as it was to decide to go off it and try fertility tracking for bc, I haven't looked back and I'd do it again 100 times. It absolutely KILLED any ounce desire for sex that I may have had. And I feel like a new me since I stopped.
Since I quit, I find myself on much more of a natural rythym, whereby at the beginning of my cycle through ovulation, I do actually desire and enjoy sex. After ovulation, that desire wanes a bit, so I do kind of go through the motions for those 2 weeks, but it is not nearly as bad as when I was on bc. I don't feel those strong feelings of 'violation' that you describe anymore. Then, as soon as my cycle restarts, I'm right back to desiring sex again. It's rather primal, actually, desiring sex during the time period in which one can conceive. Anyhow, since being off bc, this pattern is extremely consistent, so I do *enjoy* sex at least 2 weeks out of the month, and the other 2, well I don't hate it like I used to. Heck, sometimes, I even enjoy it then too...
The other thing I do sometimes, especially if it's in that 2 week period when I may not be desiring sex as much, is have a glass of wine to relax. This will sound contradictory, but I do not drink. I don't go to bars, I don't order a drink with dinner, I just don't ever drink. But I found that having a bottle of wine in the house, where I can have glass after putting my son to bed, allows me to relax a little, move into adult mode a little, and just ease into a different mindset. I don't always have a glass of wine, and I never get intoxicated, but sometimes, if I feel like my finance might be wanting a little more of me, and I might be feeling a little resistant, a glass of wine does help me to relax and not be so uptight. It might seem counterproductive if you are tired, to drink a glass of wine since that can make you a little drowsy too, but I don't find that to be the case as much... I find it relaxing, but not necessarily sleep inducing, since I'm not drinking all that much.
Best wishes to you... I can definitely relate on a very personal level, and it is a true struggle. Don't beat yourself up about this because most likely there are things you can do to change things up, at least a little. Lastly, don't discount the NORMALCY of your feelings, with 3 little ones at home. That is soooooo normal to have sex as the LAST thing on your mind. That, coupled with your bc, and perhaps post partum hormones - well, that combo is a veritable recipe for disaster as far as sex drive goes!