I am a single parent by choice. And by adoption
In my experience about 85% of adopters express a preference for a girl initially, including me.
I am now the proud parent to an 11 year old boy.
Many people change their mind about trying to dictate a sex preference when they realise that it could delay matters quite substantially. As you are literally wiping out half of the possible available children and outside of China the demand for girls is such that you will wait longer (sometimes quite substantially longer) for a girl or might have to compromise more on other things you might not want to.
Of course some people have a marked preference for one sex or another and sometimes for quite sensible reasons (though more often not)! Your reasons (possibly unwittingly) partially citing what mother/son relationships are like, verge on sounding rather creepy to this mother of a son. I don't think it's particularly healthy for you to carry these attitudes around even if you go ahead with sex selection in a possible unregulated country/clinic.
As someone upthread pointed out - girls need healthy role models too and I'm not sure your current thinking is a particularly healthy one.
The air of desperation that things must be a certain way or you couldn't cope with them is not in my opinion very compatible with the stresses of what it is actually like to cope as a single parent from day 1. Whether you end up still wanting a girl or not, I would strongly advise you try to deal with these issues before you deal with the challenge that is single parenthood.
Though quite how you do that as you are so adamant that counselling doesn't work (none of it?!) escapes me.
Sorry I can't be more help on the practicalities - I've had IVF and looked into any number of other options, egg donation and embryo adoption and IVF in other countries but never considered the clinics that were prepared to do sex selection for social reasons to be ethical enough to be safe for my child.