Right lo is in bed can reply properly now!! Poo wise I've had a few green/yellow poos that are stringy and have lumps of cottage cheese in them I've just assumed its ok as he seems fine in himself, but it does tend to happen more when I've topped him up with formula.
When my lo was 8 weeks old he dropped weight and I was told by my hv to add a formula feed, I was really set against it as I felt it would make his colic worse and contribute to a diminished milk supply, my mum was over the moon as she hates me bf and is always saying I can't wait until he's on formula and I can give him a bottle (she could give him a bottle of expressed milk now but she doesn't think that's the same!!!!) She even said she would by some aptamil and give him it, I went mental and said she'd never see lo again if she did that! I don't know what is up with people like her and your mil but it really riles me, we've made a choice to bf so GET OVER IT! What I hated most was the look of satisfaction when hv suggested a formula top up, like see I told you it was wrong to bf!
Anyway I stuck to my guns and did everything to increase my supply and did loads of skin to skin to encourage a good latch and fed him from one side until I was sure he was getting the real hind stuff. It paid off and he was weighed today (first time since the drop at 8 weeks) and he's jumped from 9th percentile to 25th!! I'm chuffed and glad I listened to my instincts. Im also glad he wasn't weighed in that time as I'm sure with all the spurts and teething he's done there would have been fluctuations in his weight and I'd have only worried. So it all evened out in the end for us and it might for you too?
I have given lo the odd carton of formula at bedtime when he hit his big spurt at 3 months & 4 months but it was only cos id run out of expressed and my supply hadn't caught up to his new demands. I don't like doing it tho as I know he gets more calories etc from my milk but I'd it helps fill his belly before bed for a couple of nights then needs must.
I don't think your problem is supply, I think its that she isn't taking enough for whatever reason, bf babies know how much they need and you can't overfeed them, so if the supply is there and she isn't screaming in hunger for more then I don't see why they have recommended formula??? If she manages to take more from a bottle than you then it might be worth doing a bottle of expressed hind milk once a day so you know she's getting it. Try working on her latch, maybe she's not quite on properly and so she's getting tired with the effort to get some milk and falling asleep, this was part of the problem with my Lo he was feeding loads but not very efficiently, he still feeds loads but he's getting maximum milk!