Provided the mum had the child's passport, and the dad had made no application to court, she almost certainly could remove the child from the UK - all she'd have to do is say she was going on holiday. Technically this is child abduction (as she'd be leaving the country with a child but without either a residency order, permission of all those with PR, or court-ordered Leave To Remove) but it's very unlikely she'd be stopped. If she did get out of the country with the child and refused to return then the dad could apply to court to get the child back to the UK - I don't know the details of how that works or what the likelihood of a court agreeing is.
If the dad believes there is good reason to fear that the mum could abscond with the child then he could apply to court for a temporary Prohibited Steps Order to stop the mum doing this until the case can be heard properly in court and a decision made. There's also a way of sending notice to ports saying that permission has not been granted for a child to be removed from the country - there is a specific name for this and, for the life of me, I can't recall what it is. FNF can advise.
Once it does get heard properly in court then the court could decide that it's in the best interests of the child to go with his mum to Romania, in which case (as I understand it) the court would award the mum sole residency, grant her Leave To Remove, and probably try to sort out a Contact Order for the dad so there is a set schedule for the child to see his father. Or the court could decide it's best for the child to stay in the UK with his dad.
I'd say there's a good case for the child staying in the UK but these things are far from certain. If the sexes were the other way round (ie, if it was a mum who was the full-time carer, the dad worked, they split and the dad wanted to take the child overseas back to his country of origin) then he'd have no chance whatsoever of getting a court to agree. As it is, though, it's impossible to be so certain.