If I'm understanding this right, I'm really wondering what his real reason is for trying to persuade you to give up your military career. Play out in your head fully and completely ALL possible scenarios to both staying in the military and getting out (play out both your reasons then his reasons). Which one gives you a better feeling? Try to remain as objective and FAIR as possible when you're playing out the scenarios. Blame is small-minded and shouldn't be a factor.
The care that your daughter gets should be a top priority for you and you need to take care of that. You have help - JAG and legal services. Find out exactly what the requirements are for getting your daughter stationed with you if you think her health isn't being cared for. You'll need proof so you'll need to get that FIRST before any non-care issues are covered up quickly. Is there another family member she could stay with temporarily? Could someone take pictures of her teeth and overall appearance? Do not give your child's father a reason or excuse to claim that you are an unfit mother. Being a service member does NOT make you unfit and you should fight for yours and your daughter's rights to be together.
Be strong and proud and courageous in your personal battles. Remember, you can make an appointment with legal services to find out exactly what you CAN do. As a veteran myself, I am humbled that you are serving your country proudly. It fills my heart with pride because, as you will come to know, once you wear that uniform, no matter what your station in life, you are ALWAYS wearing that uniform. Wear it proudly in every aspect of your life. Show your daughter what her mother is made of.
Getting out of the military is certainly an option but not the only one. The military life can be a great environment to bring up your family but it's like everything else in this world, you have to be mature enough to recognize the good and bad of it and make a solid plan and follow through on the daily stuff. Lonely military wives can be extremely negative so I wouldn't hold much of their 'information' and 'advice' to heart. You decide for yourself. I think any military person who is serious about their family will be an example of leadership for the rest of the military families out there. And who knows, you just might meet another military member who is serious about taking care of a single mom and her little girl :)