Can Priests Adopt Children?

[Woodstock]

I think most of this has to do with when the discernment for family/priesthood comes into play, but I am not sure.
For instance, in the eastern rite I believe they must be married prior to ordination, after ordination the door shuts closed on that possibility (if I am correct on this) so, with your desires being both to have kids and be a priest

(cont)

It is true that the Eastern churches allow married men to be ordained. The canon laws also forbid their remarriage in the case of death or divorce. Sadly, the latter is a small but growing problem among some Orthodox jurisdictions in western lands where the priests have large parishes and few fellow priests to assist. The Eastern model is quite the opposite with small parishes and many clergy assigned to each (including minor orders). This is not a growing problem in the Eastern Catholic Churches because they have another sad dilemma in that they rarely ordain married men at this point in time. Those they do ordain are generally older and have typically finished raising their families. Pray for an increase in vocations, both married and celibate, and both for the east and the west!