The only source for this statement I could find is a narration from sho'ab al-Eman of imam al-Bayhaqi. In al-Bayhaqi's book it is qualified as hadith mawquf حديث موقوف (a saying of a sahabi). According this blog post it is disconnected.
Here the hadith with the full chain as is in al-Bayhaqi's sho'ab al-Eman:
أَخْبَرَنَا مُحَمَّدُ بْنُ أَبِي الْمَعْرُوفِ الْفَقِيهُ ، أنا أَبُو سَهْلٍ الإسْفَرَايِينِيُّ ، نا أَحْمَدُ بْنُ الْحُسَيْنِ الْحَذَّاءُ ، نا عَلِيُّ ابْنُ الْمَدِينِيِّ ، نا إِبْرَاهِيمُ بْنُ عُمَرَ ، نا مُحَمَّدُ بْنُ مُسْلِمٍ ، عَنِ ابْنِ أَبِي نَجِيحٍ ، عَنْ أَبِيهِ ، قَالَ : قَالَ عُمَرُ : " لَيُعْجِبُنِي الرَّجُلُ أَنْ يَكُونَ فِي أَهْلِ بَيْتِهِ كَالصَّبِيِّ ، فَإِذَا ابْتُغِيَ مِنْهُ وُجِدَ رَجُلا "
Muhammad ibn abi M'aruf (the faqih) informed us, from abu Sahl al-Isfaryyny from Ahmad ibn al-Hussayn al-Hadda' (the shoe maker) from 'ali ibn al-Madini (a known hadith scholar, contemporary to Imam Ahmad) from Ibrhaim ibn 'Omar from Muhammad ibn Muslim from ibn abi Najih from his father who said 'Omar said ...
Ibn abi Najih (died 134 a.H.), his father Yassar al-Makki يَسَارالْمَكِّي (died 109 a.H.) has narrated from ibn 'Omar (directly and indirectly according at-Tirmidhi whon affirms that he has met ibn 'Omar), but this doesn't confirm whether or not he met 'Omar ibn al-Khatab. The Sheikh Abdusallam ibn Mohsin aal 'Isa الشيخ عبد السلام بن محسن آل عيسى qulified this narration as follows: "The sanad of this narration is a mix between trustworthy ثقة (thiqah) and righteous صدوق (sadoq) narrators, with the exception of the teacher (sheikh) of al-Bayhaqi himself Muhammad ibn abi Ma'ruf for whom I didn't find any biography and the chain is disconnected from the narration of Yassar al-Makki (who indeed is thrustworthy)from 'Omar, so the hadith is weak (da'if )"
It was apparently also quoted by ibn 'Asakir in his tareekh Baghdad based on the narration compiled in the book al-Mujalasah of the maliki scholar Ad-Dynawri الدِّينَوري. Here the hadith with the full chain of ad-Dynawri:
إبراهيم بن دازيل الهمداني نا أبو حذيفة عن الثوري عن أبيه عن إبراهيم التيمي قال كان عمر بن الخطاب يقول ينبغي للرجل أن يكون في أهله مثل الصبي فإذا التمس ما عنده وجد رجلا
Ibrahim ibn Dazeel al-Hamadani from Abu Hudaifah from at-Thawri (the Imam) from his father from Ibrahim at-Taymy who said 'Omar ibn al-Khatab used to say ...
The issue is that even if Ibrahim at-Taymy (died 120 a.H.) is known to narrate on the authority of 'Omar as written in syar 'alam an-Nubala' of imam a-Dhahabi it is rather doubtful that they have met so the chain can be considered as disconnected.
So far what the blog says maybe here and there with my additions.
I'd like to say that the fact that two different chains report the same thing should give the statement and content a certain value, we will never be able to qualify 100% any statement, so we don't really know whether it is correctly attributed to 'Omar or not, but you may find it quoted in so many books (on hadith, tafsir, marriage, relationship between husband and wife) that it seems to have been adapted. On the whole it goes ahead with the statements of the Prophet () in the sahih hadith:
..."Why didn't you marry a young girl so that you could play with her and she with you?"... (sahih al-Bukhari)
And in other hadith compilations:
... Everything with which a man amuses himself is vain except three (things): a man's training of his horse, his playing with his wife, and his shooting with his bow and arrow.... (sunan abi Dawod and an-Nasa-i)
The context of this narrations is the relationship a husband should be nice and with a good taste of humor so the child or boy in him should be shown off in front of his wife, but if it comes to serious matters he should act like a man! Our Prophet used to race with his wifes, and joke even in the "bathroom".