One of my employees in a tech startup is behaving erratically. We are a small team of about a dozen people working our asses off for launching our apps. Initially he was ok, working and trying to learn. But now he seems a bit disinterested. some of the problems we are facing with him are:

1. His father has a terminal illness so he has to visit his parents. We are fine with it. He goes on Friday and comes back on Monday. All other members work on saturday and sunday if required but given his exceptional circumstances we are okay with it.
2. Quite regularly he just tells my boss that he is in a bad frame of mind and needs to reinvigorate for which he goes to his girlfriend's city, stays there for a week and comes back. My boss is very pissed and I don’t like that he directly approached him instead of taking my approval. We are a small team so everyone is approachable.
3. A few days back he came up with a plan that since he doesn’t like the city we have an office in he can work from home in his girlfriend’s city. This was also done directly to my boss. My boss talked to me and conveyed that we should start looking for someone new as this will not work. I intervened and talked to the employee and suggested that he could work from home for a week but he has to be in our office for the rest of time. I do not want to ask him to resign as I think he can improve if he focuses and shows commitment.
4. So he went for his monthly leave and came back and did not do any work. He was supposed to be working from home. Seeing his slow pace I finished off his tasks. He came up with excuse that the data card given was not working. I mean in this age of hotspot and tethering… I swallowed my frustration.

I really do not wish to fire any of my employees but in a small team we cannot be giving too many freebies to one employee otherwise other team members will start feeling discriminated. Also we are output driven so he should at least deliver on tasks assigned and agreed on.

So I am in a bind: How to make him understand that being adults we have to deal with our problems and work or we take leave without pay. One cannot be doing nothing for weeks and expecting to be paid.

EDIT:
I talked to the employee... and mentioned that his output has declined substantially over past two months as compared to his first two months (only 4 months old). He was evasive but when pressed he admitted that this city is not conducive and he would like to work in another city(neighboring his gf) and he gave me a deadline that he will resign by 31st May.. i calmed him down and asked him to take his time and look for a job he wants and not change another one so fast (this is his third job in 2 yrs)... he has our support and even if does not leave we will be fine but he has to perform and meet mutually agreed deadlines... keep us looped in of any difficulties which can result in output decline... no breaking the hierarchy and show commitment and dedication till he is with us...