1) DON'T PANIC!
2) Don't, I repeat DO NOT go, unless you feel you must. The Singapore govt. are going to say that you must - but as a British citizen I would have thought that they would need you to agree to this. Bear in mind that agreeing to this could lead to further obligations eg active service in the event that Singapore enters military conflict. Furthermore the army isn't the place to be if you are percieved to be an outsider.
3) Get some good independent legal advice, The CAB should be able to point you in the right direction. The FCO might be helpful but that depends on their policy and relationship with the Singapore govt. If you don't like what you hear don't just accept it. Family issues aside, I can't see how you can be legally forced to go, the only issue would seem to be your legal position if you chose to go to Singapore.
Be on the ball about this, don't just ignore it and don't just walk into it blind.
HTH Good luck!