I am currently employed in one company with 2 weeks notice period (been working here for 2 years), I also signed a deal with another company, telling them I have 4 weeks long notice (I actually thought I had at the beginning).
So right now I have 2 weeks left to tell about my job change at my current company. I've been thinking about taking 5 - 10 days off to travel somewhere, then come back, resign, and go through my notice period. Is something like that acceptable?
Why not just give your 2-week notice now and travel the two weeks after separation from your current company? At least in my part of the world (where you get paid for accrued vacation time), this is financially the same.
That's the normal, professional, thing to do and doesn't mislead anyone. You wouldn't be burning any bridges this way.
It's pretty common for people to want some down-time between jobs. Most people handle it this way.
Taking holidays before you give notice is totally acceptable. In the USA, companies tend to not respect the holidays that you deserve, so taking them before you give notice would be recommended.
Know the company policies about vacation and how they pay it out.
If they pay you for unused vacation then you may decide that giving notice, then working the two weeks, and then using the payout to fund your time off before starting the new job makes more sense to you.
Of course if they don't pay for unused vacation, then your plan of vacation, give notice, work for two weeks, and then start the new job is the preferable plan. It maximizes your benefits and it also has the benefit of delaying giving notice as long as possible. It the United States it also has the effect of minimizing gaps in insurance coverage it that applies in your situation.
Do you really believe it's a good idea to start a new job with a lie about your old job's notice period? What if you end up adding some colleagues or even your supervisor on social media where you posted nice vacation photos? It's probably not the kind of lie that can/will get you fired but it will leave a bad impression for sure.
Since it was an honest mistake, I'd contact whoever's your contact at the new company and tell them that you realized that you only have a two-week notice period but that you'd prefer to use the two extra weeks for travelling instead of taking paid holidays from your new employer for that.
They might have already started planning for you to start only in one month so chances are good they'll take it as a sign of you being honest with them and won't mind you keeping the start date you initially negotiated.
