Ah 12 weeks, such a frustrating age for sleep! I'm glad to hear you're not in favour of CIO. I'm sure you know but we don't support that technique here as Tracy felt it breaks the bound of trust between parent and child. It's really important that you and DH are on the same page, otherwise your LO will become very confused and anxious. 10-15 minutes is quite a long time for a baby to be left alone and crying. It can be very a very frustrating time and if you're not around to replace DH in his moment of exasperation, that may just be what has to happen. It is better he takes a moment than lose his patience with DD. However if you are at home, it would great if you could pop in for those few minutes so everyone is supported.
On to your question. If you're able to move your LO to the bassinet for nap times, even just one to start, that will likely help considerably. At the moment, it sounds like the swing is her preferred sleeping location because of the movement. Something that worked well for me around this time was putting in DS in his full swaddle and then into a sling to help him fall asleep. It was still motion but not as consistent as the swing because it was just me moving around. Once he fell asleep, I would slip him into the crib to sleep. The difference is that DS was in his own crib from 2 weeks old, I'm not suggesting you do that, it's just what we did. I do believe that if you can get DD to nap once a day in her bassinet, preferably the second nap so she doesn't forget the space at bed time, that will help. Once you get one nap in the bassinet, try for two but give her time to adjust.
HTH!