Upvote:2
lay Catholics are allowed to marry non-Catholics, but is there a special rule for priests
No, there is no "special rule for priests" allowing them to marry. Catholic priests cannot marry, though married men can become Catholic priests.
Upvote:2
The question appears to ask whether those married to non-Catholics can be ordained.
Yes. There is no special restriction on ordination.
Married men can only be ordained with special permission from Rome. (Canons 1042.1, 1047.2.3).
A marriage is indeed invalid when "one of the two persons was...received into [the catholic Church] and the other was not baptised." (Can. 1086.1) but this impediment can be dispensed (Can. 1086.2) provided that various acts have taken place (Cann. 1125, 1126) regarding the danger of defecting from the faith and the raising of any children. Once a potentially invalid marriage is confirmed to be valid, there is no bar to receiving the sacraments, including ordination.
Note that this is not specific to the Ordinariates. It applies to any Catholic priest, and there are a number of married priests outside the Ordinariates.