You would think so wouldn't you, after all, it's your money!
In practise though, it's not as easy as you might think because anti money laundering and anti fraud laws mean you generally have to withdraw money to the same account you funded your trading from.
Some forex trading account providers will allow you to fund from multiple sources, but then insist on putting money back to those sources in some proportion or some order or other.
Some forex trading account providers at least claim that they may, AT THEIR DISCRETION, let you do it, IF the destination account is in the same name, but I wouldn't be surprised if they charged you for it, and actually the charges might be somewhat justified if they have to invoke identification procedures to make sure the other account is indeed actually you.
You would have to talk to a specific service provider and see if they agree to do what you want, they all have FAQs about funding and withdrawal so you can scan around online for the slightly more flexible ones and then give them a call. You might find it difficult to get any guarantees out of them though.