Ds (now 11mo) was having bad problems with his bowel around 4,5,6 months and we tried dairy (then soya, then egg) free diet (first for me as he was ebf, then for him once he weaned iyswim). We still don't know for sure but assume he was suffering from intolerance (interestingly the blood allergy tests didn't show any actual allergies, but the paed said could still be intolerance). We are now reintroducing although numerous colds, viruses and bouts of d and v over winter have delayed this a bit so for the time being he still does without all those foods as do I while still bf. Early on I asked to be referred to a dietician and she is wonderful. She is happy for us to call her any time with questions, worries etc and she provided excellent checklists to help with label checking etc. as well as recipes and meal ideas. I would definitely, definitely recommend you ask to see one if you think the dairy free diet is making a difference.
Ds has never tasted cheese so doesn't miss it, but he has lots of ham, hummus, banana and bread with pure (sunflower). He also likes peanut butter although I don't let him have too much! Meal ideas - there are loads of great recipes online you can try huge other day I made a cheese less lasagna which was surprisingly tasty! He likes trout pasta (just smoked trout cooked with courgette, mushrooms and olive oil then mixed with pasta) and today tried lamb mince bolognaise. Oat milk makes a great white sauce, coconut milk is ace for Thai style dishes including rice pudding (mix coconut milk, pudding rice, sugar and cardamom pods and cook for about an hour), yum. Tesco also sell a chocolate oat milk in their uht milk section which you can warm through to make hot chocolate. You can also use birds custard powder (the old fashioned kind, not instant powder which does contain milk) with eg coconut milk to make delicious custard. (Tis is more for me than ds as hes still not 1 yet, but I let him try it as a special treat!). I've found some great vegan bake recipes on line so plan to batch cook and freeze some cakes etc for him, eg mini carrot muffins.
Bread is one of the hardest as so many contain milk/soya but Waitrose stoneground whole meal is free of both and our favourite.
I can't comment at all about the movicol, definitely worth discussing with his doctor if you can. But I would say (ahem, tmi alert) that without dairy (and I used to be a cheese addict!) my, ahem, system, is a lot less sluggish (to use the euphemism favoured by constipation remedy adverts) than it used to be.
Whoa, long post! But I hope some of it is helpful!