Being up front and honest would be better in the long run, rather than getting the training and then saying, I'm going to be out for X weeks/months. Trying to deceive a doctor will possibly make your employers think you are deceptive in other ways.
Are you afraid that they will fire you entirely? Or just that they will turn you down for the training and you'll still have a job but won't advance (for now) and wont' make full-time? It's not clear from your post. You say you would later "take maternity leave where I would be safe from being fired." Fired as a part-timer or as a full-timer, assuming you would be full time after the training?
I'd go to HR first and talk with them what your rights (if any) are. But most of all I'd tell the truth now and if you want to keep working and eventually be full time there, tell them that very clearly and tell them about your specific plans for child care, how long you would need off when the baby is born, etc. You do have those plans in place--don't you? I would think they'd be likelier to stick by you if you are crystal clear about your plans and intentions and make them feel you really do want to commit to them. They may deny you the training just now but say you can do it later, after maternity leave, for instance (and hold them to it!).