<human>: Give me a shortened version of the text

I apologize in advance if this is not the appropriate forum for this kind of question. 

I graduated with a BS in an engineering field this May and have been hired at a government lab. The job will required a that I complete a background check before I can be cleared to work because they need to know if I can qualify for security clearance later. I filled out the paper work a few months ago with little idea of what my summer would be like. When asked about a start date, I mentioned August 1st. However, as is fairly common, I now have a problem with that date because of a girl. 

This particular girl is very special to me and I do not want to lose her. The problem comes from two things, first she is living in Prague, and second she has several psychological issues (bipolar and others) that make it difficult for her to live there alone (without me). My choices are these: I can begin working at the Lab on August first, like I filled out in the form, and then she would most likely not be able to stay in Prague safely because of depression. She would come back to the states, blame me for not being with her and choosing work over her, and I would loose her. Or I could go to Prague for the next 2-2.5 months and probably give her enough strength to stay for the duration of her stay, however I would miss the original start date with lab by many weeks. 

My questions is how to (or whether to at all) bring this up with the lab. I don't know this kind of career etiquette at all, so I don't know if this is wildly unprofessional and could cause them to retract their offer to me (another thing that I am not willing to loose). Is it acceptable to ask for a 6-7 week delay in my start date?
<bot>: I want to push back a start date 4-6 weeks from when I said I could start because of a relationship. Is that possible? should I even ask?