You know her from the last two years and if you find her healthy then there is nothing to worry. Moreover, you can use a condom to avoid such STDs. If you use a condom then there is no chance of you getting infected. It appears to be that you have so many misconceptions towards the STD and you have read so many articles without understanding it properly. Two years are a good amount of time to know about the health of other person. Stop thinking too much if you want to have sex with her otherwise, stop meeting her and let her find another man who fucks her daily.
The depth in the relationship that makes a bonding in between partners for sex. Its good that you want to confirm about the transmission medium and other details of the STD because you have a precautionary clause with you. You should tell us what type of relationship you are maintaining for last 2 years. This explanation will lead to further look into the other angles.
You have to convince her about the importance of the lab test to confirm about the STD. If she is not agreeing then you have to convince her. The alternative way is to use the condom regularly because she may be good by look who knows about her physical relationship or his husband’s. Her husband allows her to have affairs with you means she approved your relationship that indicates negatively.
Unsafe sex is always attracts chances of infection so be careful about the next course of action.