Are there any amateur radios that can transmit on ham banda and that is legal to transmit on frs and gmrs( if you have license)
No. None of the amateur radios are legal to use on GMRS. They do not have the necessary FCC type certifications. You may have people tell you that they can be modified (often called a MARS/CAP mod), but that doesn't address the FCC type certification issues.
If you want one radio that does Amateur and GMRS —legally—, then you need to get a commercial radio that has the FCC Part 95 certs and program in some amateur frequencies.
-However, none of the commercial radios are going to have the VFO function that amateurs like. There are some that have "front panel programming", but activating that feature would legally void the acceptance for GMRS use.
-Also, if you want dual band, VHF/2 meters and UHF/70 centimeters, you will need to stick to the amateur radios, unless you have a several thousand dollar budget.
For a new ham, I get the idea to buy a low tier radio like the BaoFeng, but ultimately you'll have some disappointing experiences with them. No matter what anyone tries to tell you, they are 'junk' radios. Limited amount of filtering on them make them susceptible to interference. The transmit audio on them is often pretty bad, to the point that I can often tell when someone is using one. They are also "disposable" radios, as in if something goes wrong with it, you toss them in the trash, as they cannot be repaired.
Getting a basic radio from Icom, Kenwood or Yaesu, if your budget allows, will be a good investment in the long run. The radio will be easier to use, you'll have less issues, and a better chance that local hams can assist you with things like programming.
