Bees will teach you patience. There are no short cuts.
But remember that the bees themselves have no patience whatsoever.
The rate of brood rearing is usually limited by the amount of beepower available to keep the brood warm.
If you managed to find and remove a virgin and successfully introduce a mated queen to one group (note that is two big 'if's there), then that group might only be a single week ahead of the virgin-led group. Princesses mate earlier in small colonies - one reason for Apideas!
Better to keep them apart until you know what you have got (and that they are healthy). Or else combine asap and put all your eggs in one basket and bees in one hive - I'd only recommend that if either was really pathetically small (a double handful or less).
However, a full hive is much too big for a small colony - one function of nuc hives! A simpler option would be to use dummy boards to restrict their scope. Warmth is important, so insulate above (though a polynuc would be even better) - and after a couple of days feed all they can take for a week or so.