There are people who have Developmental Coordination Disorder (or dyspraxia) who don't have speech issues. The kid who plays "Harry Potter" (Daniel Radcliffe) has dyspraxia...you would never know it watching him in the movies.
I am not sure where you are located (in the US?)...but we ultimately had a neuropsych diagnose DS with DCD, then we took that eval to the school system and told them we want a school evaluation. They ultimately put him in the "physically impaired" spec. ed category, which is fairly flexible and he qualified for adapted phy ed, and OT (among other things--he already had a speech IEP). He gets regular phy ed in addition to the adapted phy ed. He had to test something like 1.5 or 2 standard deviations below the mean on a test of motor development to qualify for adapted phy ed (or DAPE). Has your DD had a test of motor development like the BOT? The private OT/PT did the BOT but the school did another test of gross motor skills where he scored even lower (I can look up the name if you want).
I have mixed feelings about OT and how helpful it has been. I think DS benefited a lot more from private PT than OT. Most of it I feel like I could have easily done at home myself. But we had insurance coverage and it's easier to get cooperation from DS from anyone but me, so we just went for it(we had an $18-23 co-pay so it wasn't bad). I did watch most of the sessions so was able to see that there was nothing magical about what they were doing, and was able to incorporate it into what we were doing at home. So that might be an option for you. A good OT will actively train the parents and give you exercises to do yourself, because most of the benefit will come from what is done at home.