Police were called to a report of an accident on Track Road at 12.46pm.
The woman’s injuries were confirmed as "serious but not life-threatening", said police.
"The child did not have serious injuries," said a spokesperson.
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Enquiries are ongoing to establish the circumstances of the incident.
Anyone who saw what happened or the circumstances leading up to it is asked to call West Yorkshire Police on 101, or via the 101Chat function online at www.westyorkshire.police.uk/101livechat, quoting reference 740 of 4/7.