そんなワケねーだろ、このめでてぇ日に

The person who said this line is known for using katakana instead of Hiragana
or Kanji. I've found some other conflicting definitions for ウケ but none seem
to fit the context of the above sentence. On a side note I assume めでてぇ is a
casual form of omedetou?
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question
meaning
What is the meaning of ワケ in this sentence?
> "そんなウケねだろ"  
>  ="そんな + ウケ + ね + だろ"  
>  ="そんな（のは） + ウケ + ねぇ（not） + だろ"  
>  ="そんな（のは）(such story) + ウケ(appeal) + ねぇ（not） + だろ(perhaps)"

This "ね" in this context is the abbliviabion of "ねぇ"="ねえ"="ない"

"ウケね" or "ウケねぇ" is a spoken rude language.

The following use of "ね" is entirely different from the use of the above
example.

"今朝は寒いね" It's extermly cold this morning.

"ね" here is used for other's consent.

> "今朝は寒いね"  
>  "本当！今朝は冷えるね"

The reason why "ウケ" is in Katakana may be the speaker avoid the sequense of
Hiragana like "そんなうけねだろ" to make the word "うけ（る）" clear in the written
sentence for the reader. "そんなうけねだろう" is also acceptable.

Generally the word "そんな" could be "そんなには(それほどには) less than expected" or "そんなのは
(being foreign to something)." The latter is the case in the context of your
example sentence, "being foreign to this happy day."
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answer
The "dictionary" form of:

> 「そんなワケ **ねー** だろ、この **めでてぇ** 日{ひ}に。」

would be:

> 「そんなわけ **ない** だろう、この **めでたい** 日に。」

The original phrase is in the **_Kanto tough guy speech_**. Occuring twice in
that short phrase is the "famous" あい-to-えぇ/えー switch. 「ない」 became 「ねー」 and
「めでたい」 became 「めでてぇ」. This phenomenon has been discussed many times here on
SE, so I will just leave it at that.

「ワケ/わけ/訳{わけ}」 here is somewhat difficult to translate all by itself, but if I
had to, I would go with "reason" or "ground".

I would, instead, suggest that you remember 「そんなわけ（は/が）ない」 as a set phrase
meaning " ** _said no one ever_** " if I could go somewhat slangish. To use a
more traditional TL, it would be " ** _there is no way (that is
true/possible)_** "

This phrase is used very heavily among native speakers. You will often hear
the more slangy form 「 **な** わけねーだろ」 as 「そんな」 is often contracted to just 「な」
in very informal speech.

> On a side note I assume めでてぇ is a casual form of omedetou?

No, it is not. As I stated above, it is the same as 「めでたい」.

So, the phrase in question means:

> "There's no way that's possible on a happy day like this!"

Provide more context if this does not sound right.
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answer