I am a Belgian citizen and here in the USA to spend the holidays with my daughter's family. I have ESTA and allowed to stay until Feb 23, 2017. My daughter has submitted a petition for an alien relative (that's me) (I-130) and is still underway. Should I leave before my 90 days or should I wait for the result of my daughter's petition. Note: The petition application did mention Feb. 23, 2017 as the last day I am allowed to stay.
You didn't mention what is your plan for immigrating.
If you want to immigrate without leaving the US, you guys should have filed I-130 and I-485 together. If you didn't file I-485, you can file it now with the I-130 receipt. Filing the I-485 should generally allow you to stay (although it's somewhat tricky when you're on VWP as you cannot challenge a removal). Filing the I-130 petition by itself doesn't give you any ability to stay.
If instead you want to leave and go through consular processing at the US consulate abroad for an immigrant visa, then you wouldn't do anything now and leave and contact USCIS to have them change the petition from Adjustment of Status to Consular Processing (since they assumed you were going to do AOS because you were in the country).
Exchange before your time is up. Adjustment of status under ESTA for immediate relatives of petitioners (like in your case) have previously been approved however many have also been denied.
What is particularly dangerous about trying to adjust status while under ESTA is that if it is refused, you have no right to appeal or go before an immigration judge and you become removable immediately your petition is denied. See USCIS memo in the link.
For this reason, if possible you do not want to try to adjust status under an ESTA. It is better to go back to your country and go through consular processing, or to return with a visa.
All the best.