They probably would know that she had sex if the vet examined her down deep in there. But I doubt they would be able to tell whether it was a dog or you. Unless she is full of your cum.
Even then - none of their interest. Just say that you got male dogs as well and topic is done.
No veterinary has time to analyze the type of sperm or anything like that. They mostly wouldn't do it in-house anyway but send it to a laboratory.
What could give them a hint is her behavior if they check her vulva on inflammations as example, but even then they will in 99,9% of the time not really combine 1 & 1. And if they do, then they mostly don't talk about it.
There's no profit to generate for them by blaming pet owners of obviously well-cared animals with guessed constellations that they can't prove. After all you are their client, their money bag, not your dog (so harsh this might sound from a zoo's perspective).
Veterinaries can suggest the customer (= you) things, but if they keep annoying the customer with procedures that he/she declines, then they might quickly loose that customer. It's that easy. And spaying / neutering has side effects. Quite a lot, to be honest. And some of them are not even told or mentioned by medical books, neither deeply analyzed due to no "problem", more of a "nuisance".
This is enough for anyone who wants to not spay / neuter their pets to decline it. Just tell a veterinary, that you had dogs in the past which lost their appetite mostly, which got uncontrollable fur growth and irregular fur change, means: the fur sticks for long time spans & regrows round the year and it can make combing a big mess (additionally to the increased growth).
Incontinence can occur, hormonal imbalances with side effects to the organs, there are dozens of side effects which most vets just wave aside as they are not the ones that have to care for that dog afterwards (but can make money from the future medical problems..).
There are serious illnesses which might indicate the need for spaying / neutering. Like malign tumors. But that is the absolute exception compared to "useless side effect rich" recommendations through veterinaries of spaying / neutering. Which only fulfill the delegation of responsibility aka comfortable thoughtlessness after all.
Addendum: I know well that most veterinaries are
not ignorant to animals health or well-being. Else most of them wouldn't have selected their job, aside the cash lovers. But they suffer under the same problem as human doctors they see permanent sadness, too much worse situations. Health problems they can't cure.
So they have to keep a emotional distance to their "customers pets", same as human doctors have, to not feel burdened and basically self-depressed into a state where they can't fulfill their job anymore. And this results forcibly in a specific distance in thought and as such carelessness - they just can't follow each indication of unusual aspect in the animals, as those are still individuals.
There's not much reason to fear visits on a veterinary, just because your dog gets to enjoy sexual experiences with you. Just be normal and don't mention those experiences in any way, that would highly probably generate problems.
they can - there are various options - like a vasectomy for male dogs. Or hormone injections for bitches - condoms are not an option. Or you can separate dogs when a female is in heat, but that might lead to pregnancies if you forget to lock a door or something.
Easiest(!) way is to just separate the dogs for the few days that she is able to get impregnated. And maybe 2-4 days beforehand due to the survival of sperm in a female dog. Even this time span is after she showed symptoms of the heat for days, recognizable for anyone watching her or the ground which she might as well lick to not leave trails, very easy to recognize and quite good for precise timing.
All other ways are quite delegating of the responsibility unto the animals or some sort of preventive "thing". To separate them continuously from the first heat on for the few important days is no real problem. Walking a female dog in heat through dog parks mustn'd be, because you will cause irritation under them, but aside from that: you as the owner are responsible and everyone is able to prevent unwanted impregnation without chemical side-effect rich ways.
Addendum: There are chemical ways, depending on your country, which have a similar result as the "pill after" for human females. But those come with partly harsh side effects and are not available everywhere. Also they need to be used in a specific time span after copulation with the male dog, so.. I personally would not suggest trying such a solution.
If you want an easy way to prevent impregnation and can not prevent physical contact between intact male dogs and the female dog in heat, then I would suggest an after-surgical lick/bite protective lower body suit / sleeve for her in the time of possible contact. One of those robustly made and with closed back part (quite a few are open, be careful!) is strong enough to physically prevent copulation.. (but please take it off after you are back and you can watch both dogs again.. as it prevents the hygienic self-cleaning process of the female dog and could cause urinary tract infections worn over longer time).
