Yup there's a way to do it but there's a catch: you can't do this remotely and you can only do this with PS4 games on your Vita, not Vita games.
What you need to do is make a separate account on your PS4 unless you already have one. We'll call this extra account a decoy account, this is not the account that would normally be tied to your Vita. Your Vita games are tied to your original account I assume (because that would make sense and only way you could download your PS+ games on your Vita) so keep it that way. Now if you don't care to download any PS+ games or care to keep your original account on the Vita, you can actually play your original account on your Vita with the DS4 with this trick.
Anyway, get on your decoy account on the PS4.
Connect your PS Vita to your PS4 through remote play. It will now connect to your main account even though your PS4 is on the decoy accont.
Your decoy account will show up on the Vita. Don't press any buttons on the Vita.
Turn on your DS4 and connect it to the decoy account.
You can now play your Vita with a DS4 but only PS4 games.
(If you have another person with you, you can play two players using the Vita controls)
What you need to do is make a separate account on your PS4 unless you already have one. We'll call this extra account a decoy account, this is not the account that would normally be tied to your Vita. Your Vita games are tied to your original account I assume (because that would make sense and only way you could download your PS+ games on your Vita) so keep it that way. Now if you don't care to download any PS+ games or care to keep your original account on the Vita, you can actually play your original account on your Vita with the DS4 with this trick.
Anyway, get on your decoy account on the PS4.
Connect your PS Vita to your PS4 through remote play. It will now connect to your main account even though your PS4 is on the decoy accont.
Your decoy account will show up on the Vita. Don't press any buttons on the Vita.
Turn on your DS4 and connect it to the decoy account.
You can now play your Vita with a DS4 but only PS4 games.
(If you have another person with you, you can play two players using the Vita controls)