Congratulations on your new baby girl! 
'Feeding' for comfort is normal and, in my opinion, one of the best things about bfing. If baby is crying/fussing and you can't work out why, bfing (it's nursing really not feeding) often gets them calm while you work out what's wrong (full nappy, cold, hot, label sticking in them, tired, etc). Even if you can't work out what's wrong, guess what?, they have stopped crying 
You don't need to 'empty' your breast everytime she feeds (it's a physical impossibility for a start as all the ducts are at different stages in milk production - bit like a factory staggering their production lines so all the finished goods don't come off the line at the same time) and you shouldn't get blockages (I assume you mean plugged ducts?) from short nursing sessions.
If she wants to comfort nurse she will use a different type of suckling called 'non-nutritive suckling' and get very little milk but her body will release endorphins and oxytocin from her suckling which will help to soothe her as will your physical presence, your scent, your warmth and your heartbeat.
She is probably settling with your OH because she is getting his scent, his heartbeat, his warmth and that is soothing her but there is no trigger for her to nurse so she doesn't ask to. You can't change her biological need to nurse from her mum so it might be easier to accept that you soothing her at this young age involves her suckling but with her dad it doesn't.
Breast compressions can help if your baby slows down quickly into a feed and there are concerns about her weight/milk intake/lack of wet or dirty nappies but if there isn't it could be a bit of a faff to do at every feed.