And you might add "nevertheless" to the second clause.

It's not a typo for "No obstante cabe", in my opinion. "No obstante cabe recurso" would mean "Nevertheless, an appeal may be filed", and you would expect a comma after "No obstante", which would be a sentence adverb. The syntax would be clumsy, because you'd have two main clauses ("cabe recurso..." and "la misma es ejecutiva...") separated by a comma.

But that's not what it's saying. "No obstante" functions here as a preposition meaning "in spite of" or "notwithstanding", and "caber recurso" means "the fact that an appeal can be filed" ("an appeal being fileable"). So "No obstante caber recurso" means "Despite the fact that an appeal may be filed" or "Although an appeal may be filed" or "Notwithstanding the fact that an appeal may be filed". The sentence is saying that the court order is subject to appeal, but must nevertheless be enforced immediately, without waiting for the outcome of the appeal.

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Note added at 3 hrs (2017-02-28 08:24:08 GMT)
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It's this second use of no obstante in the DRAE:

"2. loc. prepos. a pesar de. Decía no interesarle el dinero; no obstante lo cual, murió rico."
http://dle.rae.es/?id=QpXHaj2

An example to illustrate its use with the infinitive:

"No obstante ser correcta la afirmación anterior, merece ser precisada."
http://repositori.uji.es/xmlui/bitstream/handle/10234/64192/...

And there are others in these previous questions:

"no obstante haber efectuado
despite the fact that the contract had been fully paid"
http://www.proz.com/kudoz/spanish_to_english/business_commer...

"ya que no obstante haber concedido a un tercero
even though having granted a third party
http://www.proz.com/kudoz/spanish_to_english/law_general/204...

"no obstante haber sido legalmente emplazada
inspite of the summons having been served"
http://www.proz.com/kudoz/spanish_to_english/law_general/467...

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Note added at 3 hrs (2017-02-28 08:35:00 GMT)
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"Even though" could be use here.

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Note added at 5 hrs (2017-02-28 10:20:43 GMT)
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"Lodged" rather than "filed" if you're using British English, by the way.