Yes you can open pink book in MY! Just go to your nearest Klinik Kesihatan (KK) with your IC and pregnancy confirmation. It’s free for Malaysian citizens. Some mummies do both, open pink book in MY for the cheaper checkups when they balik kampung, then continue main checkups at KKH in SG. The two don’t conflict.
Good tip to save cost: do your routine checkups at a MY KK or private clinic when you’re back (way cheaper), and only do the important scans and later trimester visits at KKH. As long as you deliver at KKH you can still claim hubby’s Medisave for the delivery. Just make sure to bring your KKH records when you go MY and vice versa so both sides know your history.