To OP:
I have a 2.5 year old and a 6 month old and rediscovered my passion for running after the first was born but it was not without it's difficulties. Here is my advice to you:
1. The first 2-12 months will be very difficult depending on lots of factors that have all been mentioned (baby sleep patterns, feeding, health of baby, etc.) Treat this time as a recovery phase, expect to miss some runs and lose some of your normal weekly mileage but spend the more time at home taking care of some of those niggling injuries, core work, PT, and things like that. Appreciate the time that you have to get out the door. If you run well that is great, but don't expect to.
2. Be very open about your planned schedule to your GF, work your running around your other obligations as a father & boyfriend. This helps prevent some possible resentment from her about your time running. She says that she wants you to continue to run but post-partum mothers will have some big emotional swings and she will see you spending lots of time on yourself and will probably become resentful at some point. Talk about these feelings with her and address them to come up with solutions that work for both of you - ignoring this will only make things worse.
3. Once your GF is up for it encourage her to schedule some time to do something for herself multiple times per week for an hour or two while you watch the baby. This will give her some time to have some adult interaction or catch up on some sleep and you can also build a relationship with your child and she will feel more comfortable leaving the baby with you or others as time goes along.
3a. Get a good jogging stroller (I have a BOB and double Thule), and run with your kid once they are big enough. It gives everyone a break and now is a lot of fun working on vocabulary and counting with my older one (counting dogs, naming colors of cars, things like that). My stroller miles are about 30sec/mile slower but it doesn't seem to matter to my training.
4. You will have to sacrifice some things if you want to continuing running at your level. For me it was social outings such as happy hours and nights out with friends - I wish I would have cut these things out a long time ago; they weren't adding anything substantial to my life. Much of my social interaction is now with other dads at parks or with running friends.
5. You have more time in your day than you realize, if running is really important to you then you will find time for it. Be there for your family first, but in order to be a good father/boyfriend/husband you need to be happy yourself. Take care of yourself, significant other, and child in that order have open communication and be flexible.
Remember, you will only run fast times for a few more years and nobody will really remember or care how fast you are/were in 20 years besides yourself. Your kids and GF will remember having a supporting and loving father in their lives. It sounds like you have a pretty good head on your shoulders, you should be able to figure it out. Good Luck, being a dad is amazing!