I would rescind the second offer, take it or leave it.
I had a similar thing happen with my PPOR. made an offer, got accepted, next morning agent tells me there is a higher offer, I told him they could have it,
strangely enough the second offer disappeared.
James
Same thing happen when I bought my first PPOR, said there is another buyer would I up my offer, I said sorry that is my limit and I wish the higher buyer well for getting a nice home...agent came back with something about the other buyer haven't got pre-approval and I can have the place.
almost all good sale agents has training in negotiation tactics and human finance behaviour so they can read you for who you are... a person with training can run circle around the in-experience player blind fold ...
I have similar experience so I have counter tactics...for every negotiations and tactics there are counter tactics that you throw back. Agent will pick up these counter tactics and they know they cant play you
...because they too know the counter tactics and they know they dealing with someone who has similar experience.