As I understand it, if married priests were allowed, religious orders would still retain the discipline of having their members celibate?
Yes. The vows taken by religious are different to the promises made by secular priests; and even where religious priests work in parishes, they are responsible to the bishop only in terms of the work that they do, but with regard to lifestyle and discipline remain answerable to their religious superiors.
I don’t know what the considerations would be considering the spiritual matters that Religious Orders look at,
Celibacy is an inherent part of the life of consecrated religious, and therefore would remain a necessity. However:
at least from the practical side of things, organisations whose members take vows of poverty cannot support families. In other words, just from the practical side, religious orders can’t support members with mouths to feed.
Many religious institutes do have tertiary or third order members, or oblates or associates. This is a means by which secular people can engage with a religious charism and in some cases become a canonically recognised member of an order, but they do so with officially sanctioned private vows that are suitable to their position in life – so they take a vow of chastity within marriage, for instance, meaning that they are chaste but not celibate. (Ultimately all people are called to chastity even if not celibacy, inasmuch as they are called to be either sexually abstinent or in the case of married people, considerate and unselfish in their sexual relationship).
Wouldn’t this create another problem for orders, because I would imagine, there would be even less vocations to the religious priesthood as a result? I would think that if you asked them, if a man had the choice to be a married priest or to be a celibate one, he would choose to be married.
This is a misunderstanding of the place that priesthood occupies in religious life. Although many institutes have priests as members (and some even have all members being priests), ordination is not essential to religious life itself - whereas following a rule and/or constitutions, and a charism and community life, are essential.
Typically if someone has so strong a call to priesthood, they are better to engage with the diocese, because entering religious life does not guarantee that ordination will follow (actually, neither does going to a diocesan seminary, given that the bishop may still choose not to ordain).
Religious priests are not men with a vocation to priesthood who think that community life might be a nice addition to their service to God: they are men called to service within religious life, through a distinct charism and form of community life, who are also called to serve in ordained ministry. Take their priestly ministry away, and they are still consecrated religious whose relationship with God is maintained and strengthened by the particular nature of their religious life.
In my own order, even though we are a clerical institute with a majority of priests, we believe that we are ‘brothers first and priests second’; the kind of man you describe, who clearly prefers married life to his religious vows - a choice that is not in itself unnatural or sinful - is nevertheless not suited to religious life. Consecration to God through a charism and in an established form of community living must come first for the religious, and not simply be grudgingly accepted as an unavoidable consequence of their desire to be a priest.