Hello Ceris,
I wouldn't use a rotivator for that job. You could use a rake as per Monty's video:
http://www.gardenersworld.com/how-to/projects/basics/how-to-improve-your-lawn/179.html
or if you want to use a machine, there are lawn scarifiers you can buy. It sounds as though the more gentle raking approach, involving less severing of buttercup runners, would be best for you if you can do it. Creeping buttercup and moss are both signs of poorly drained lawns, so some aeration, also shown in the above video, would probably help.
Have a look at our advice on dealing with creeping buttercup below:
http://www.gardenersworld.com/how-to/problems/weeds/creeping-buttercup/464.html
I hope you'll soon have both beautiful baskets and well-trained lawns,
Emma.
gardenersworld.com team.