Our 2 yr old has been fine with "slowly" losing his bink. We stopped the car ride one first (easiest to replace with toys, vibrations, and snacks), then the night one because he is so exhausted at night compared to nap time. Then, he started daycare 2 full days, and he gave it back to the teacher on the first day and went right to sleep! So, now we offer it if nap time is at a weird time and it might help with him going down. Oh, and emergencies like injuries out in public. But, mostly he is doing fine with the changes.
As for the crying at night when the bink falls out...you may need a bink that stays in better. Our son liked the Mam diamond textured ones as soon as he had teeth, but the smooth ones were at first easy for him to hold onto throughout sleep. We did have to get through the sleep depriving and very bumpy time of the crying out, but we made it. It was nice once he could put himself back to sleep.
Just be consistent in whatever you decide to do as a couple! We always ran into trouble when we misunderstood what our goals were for the night. We benefited by our support for each other. We would hug in the hallway, or my husband would soothingly talk me through it lying in bed. We mostly kept each other from running into his room and interrupting his process of self-soothing. Stick with what you think is best.
Something that got me through the last two years, "All I can do is what I can do."
Good luck :}