Oh, we still don't have any routines! I had DH give the bottle at bedtime because that's when he was around, during the day I just BF'd.
I didn't go cold turkey as it seemed mean.
The first couple of times he might get upset, but I would make sure your DH is giving the bottle when he is relaxed and not TOO hungry (we do BLW dinner, dunk the messy baby in a bath, then a bottle in bed, so dinner has already taken the edge off). If you've been BF'ing, your DS won't know that he can fill his tummy with a bottle or cup and if he's really hungry he will just get angry that he isn't being 'fed'. IME I don't think your mum will have any luck with the cup as he will just get angrier and angrier.
I bought little 4-oz bottles and DD seems to like that she can hold them herself. I know tesco sells a bottle-to-cup trainer that has a big rubber teat, so that might be another option. FWIW.
Another thing you might want to consider is getting your DS a lovey to sleep with. DD has a crocheted blanket from her gran. She doesn't use it as an attachment object so much as something to worry and grab at when she's trying to sleep.
I found the book "The No-Cry Sleep Solution" had a lot of good tips, but the author's primary suggestion is a bedtime routine, which we just don't do well. DD eats when she's hungry and sleeps when she's tired, end of.
Perhaps you could convince your mum to take him for one afternoon a week and give him a bottle while he is there? That would eventually get the idea in that a bottle will feed him too (and get him used to the taste of formula!) without leaving him hungry the whole day.
We did everything the very easiest way too and it was lovely. I think the semi-training we are doing now is worth the easy, lovely months . It's really not so horrible. It took DD about four or five days to adapt to the shush/pat and she only cried one time. The rest she only whinged a bit.