If you use a domain name for an iframe in your site, the browser will have to resolve it. This means it will have to make a call to DNS from the client. There is no way for you to provide the resolution to them. If you can use an IP address for the site rather than a domain name, then the client could avoid the DNS look up, but the browser would still be going to the IP address to get the content of that frame and the ISP would still know about it.
It is worth pointing out, however, that they will not know that that DNS query was related to your site. There is no difference between them having a second tab open to Google while they are on your site and you actually putting it in an iframe. They might be able to figure it out by noticing the pattern, but it would be non-trivial to notice since the iframe is entirely pulled by the client.
The only way to prevent the ISP from knowing they are using Google at all though is to pull the information yourself and forward it on like a proxy, but that would look extremely suspicious to a client under most circumstances (in addition to being very technically challenging.) Even then, you'd have to make sure you are using an encrypted connection or they might be able to recognize the content you are sending as being Google depending on how paranoid you want to be about what ISPs are doing with that information.
Overall, the risk of customer's ISPs selling information to your competitors is basically non-existent though. It's too hard to figure out who would care about which connections and then trying to sell the information. The value of the information they would have is insignificant compared to the amount it would cost them to research who would care and to try to negotiate a deal for the information. Your threat model doesn't make sense because it would cost more to exploit than the potential benefit derived from exploiting it.
Also as some business advice, if your business is dependent on your competitors not knowing who your clients are, you are probably doing it wrong. Don't spend your time making it so your competitors can't figure out who your clients are, spend your time making your product better so that your customers wouldn't want to switch. That will do far FAR more for the security of your company.