There would have to be an AGM or EGM to vote on a change to by laws. And there would have to be I believe 75 percent in favor or not more than 25 per cent against. The the by law would have to be registered (about $1,000 cost).
If the dog owners truly are in the minority get the support of the other owners. You can’t have dogs fowling common areas.
I don’t know about claiming costs from the EC. I would first approach the other owners and point out that a complex with dogs running wild and with eviidence of wear and tear and waste from them would not be appealing to any buyers in the future. I am a great advocate of pet ownership, but responsible pet ownership. Animals allowed to roam to others front doors or yards, be they strata or a free standing house, is not responsible pet ownership.