Eu doesn't have the power to directly change things, but that doesn't mean that at one point they might not put a little or not so small pressure on those not-so-liberal countries.
They have a right to family life in Latvia in a way it's written in Latvian constitution - an alliance between men and women, child and parents, a family. They are not discriminated and could win a process if they can prove they are.
They might, but I doubt they will, they have shown understanding to member states so far. Even when they had the chance to adress the ban on abortion in Ireland they declined.
Its a bigger chance that the ECHR might influence it.
And the right to a family life is not a collective right, its an individual rights, so that every individual has the right to a family life, regardless of his sexual orientation.
And just because something is in the constitution doesnt make it right... There is something above the constitution, the European Convention on Human Rights.
again, the adoptation is a difficult process that takes time and it's a problem for those older than a year - no one usually wants to take a 6 or 7 yo, not talking about 13yo. recently born - there are no problems there. by allowing gay couples adopt, you cut the chances for normal couples to adopt, because they will also prefer the youngest.
Put them all on level footing, and if the homosexual couple is a better fit they should cut chances for less fitting heterosexual couples to adopt.