ATP Hydrolysis to AMP in the Urea Cycle. What is the Free Energy Change?
The answer, I reckon, is that as stated it isn't.
However,the hydrolysis of ATP to AMP and PPi yields considerable more free energy than does the hydrolysis of ATP into ADP and Pi.
That is, the free energy change for the hydrolysis of  ATP into AMP and PPi is considerably more negative that that for the hydrolysis of ATP into ADP and Pi and for the hydrolysis of ADP into AMP and Pi.
If we consider the the free energy change for the reaction ATP  = AMP + 2 Pi  (where, say, the pyrophosphate (PPi) produced by  argininosuccinate synthetase is broken down by a  pyrophosphatase), then  it is the equivalent to  the  hydrolysis of 2 ATP to ADP and Pi and (more or less) to  the hydrolysis of 2 ADP to AMP and Pi.
When dealing with ATP hydrolysis, we must take the 'chemical environment' of the phosphate group into account, not only in determining whether the bond is 'high energy' (in the Lipmann sense) or 'low energy', but also when considering the amount of free energy released by hydrolysis of a  'high energy' linkage: not all pyrophosphate linkages yield the same free energy on hydrolysis.


Cleavage of the 'inner' pyrophosphate linkage in ATP (to give AMP and PPi) 'releases' considerably more free energy than cleavage of this linkage in ADP (to give ADP and Pi).
Cleavage of the 'inner' pyrophosphate linkage in ATP  (to give AMP and PPi) releases considerable more free energy than the cleavage of the 'outer' pyrophosphate linkage (to give ADP and Pi).


If  one 'unit' of free energy is considered to be about 32 kJ mol-1 then:

The hydrolysis of ATP to ADP and ADP roughly releases 1 unit
The hydrolysis of ADP to Pi and AMP roughly releases 1 unit
The hydrolysis of ATP to AMP and PPi roughly releases about 1.4 units
The hydrolysis of PPi to 2 Pi roughly releases about  0.6 units
Hydrolysis of ATP to AMP and 2 Pi roughly releases 2 units.
Hydrolysis of AMP to adenosine and Pi roughly releases 0.4
units.


The question posed by the OP may now be answered as follows.
Hydrolysis the inner pyrophosphate linkage of ATP (to give AMP) rather than the outer linkage (to give ADP) provides a 'thermodynamic pull' of 0.4 'free energy units' to the  argininosuccinate synthase reaction.  If the  PPi is hydrolyzed by a pyrophosphatase an extra 0.6 'free energy units' are obtained and the free energy change for the combined reaction (that of argininosuccinate synthase and the pyrophosphatase) is equivalent to 2 'free energy units' (about -70 kJ mol-1).

As pointed out by Frey, &amp; Arabshahi (1995), hydrolysis of the $\alpha$,$\beta$-phosphoanhydride of ATP, rather than the $\beta$,$\gamma$ linkage, is a common strategy in biosynthetic reactions.  To quote the final line of this paper: Cleavage of the $\beta$,$\gamma$-phosphoanhydride bridge in ATP takes place in metabolic reactions in which a smaller driving force is required.
A Small Piece of History
It was not always accepted that the hydolysis of ATP to AMP and PPi proceeded with a more negative free energy than for the hydrolysis of ATP to ADP and Pi.  To quote from  Standard Free Energy Change for the Hydrolysis of the $\alpha, \beta$-Phosphoanhydride Bridge in ATP , by Frey &amp; Arabshahi (1995).

It  appears to be common knowledge in biochemistry  that the standard free energy change $\Delta G^{'o}$ for the hydrolysis of ATP to AMP and PPi is -7.7   to  -8.4 kcal  mol-1 [-32 to -35 kJ mol-1].  Most textbooks of biochemistry  list  values  in  this  range (Zubay, 1993; Lehninger et al.,  1992; Garrett &amp; Grisham, 1994; Voet &amp; Voet, 1990; Matthews &amp; Van  Holde, 1990). Moreover, many  textbooks  also  list  the standard free energy  for  the hydrolysis of  PPi as  $\Delta G^{'o}$ = - 7.9 to  8.0 kcal  mol-1.  [-33 to -33.5 kJ mol-1]. However,  the  true  value for pyrophosphate  hydrolysis is significantly less negative (Flodgaard &amp; Fleron, 1974). Therefore, the standard free energy change for the hydrolysis of ATP to AMP and PPi must be more negative  than 8 kcal  mol-1 [ 33.5 kJ mol-1]  as is explained in this paper

This reminder should not have been necessary.  The correct value for the free energy change in the hydrolysis of ATP to AMP and PPi is given by Schuegraf et al (1960)  , a paper co-authored by Sarah Ratner
The hydrolysis of UDP-Glucose
$\Delta G^{'o}$ for the hydrolysis of UDP-glucose to UMP and  glucose-1-phosphate is about - 43 kJ mol-1 (- 10.3 mol-1) [Frey, &amp; Arabshahi, 1995], also considerably more negative that that for the hydrolysis of ATP into ADP and Pi
Specifics

The standard free energy of hydrolysis ($\Delta G^{'o}$) of the $\alpha$,$\beta$-phosphoanhydride of ATP to give AMP and PPi is about - 45 to -50 kJ mol-1

The standard free energy of hydrolysis of the $\alpha$,$\beta$-phosphoanhydride of ADP to give ADP and Pi is about -30 to -34 kJ/mol

The standard free energy of hydrolysis of the $\beta$,$\gamma$-phosphoanhydride of ATP to give ADP and Pi is about -32 to -36 kJ/mol.

The standard free energy of hydrolysis ($\Delta G^{'o}$) of PPi to 2 Pi is about 20 kJ mol-1

The standard free energy of hydrolysis ATP to AMP an 2Pi about -70 kJ mol-1.

The standard free energy of hydrolysis ($\Delta G^{'o}$) of PPi to 2 Pi is about 20 kJ mol-1

The standard free energy of hydrolysis ATP to AMP an 2Pi about -70 kJ mol-1.


(For a diagram illustrating the  nomenclature of the $\alpha$, $\beta$ and $\gamma$ phosphates of ATP, see here).
Notes

Following Alberty (2000), all equations are written as 'biochemical equations' where everything is balanced except hydrogen ions.

$\Delta G^{o'}$ for the following reaction is about -50 kJ mol-1 (-12 kcal mol-1)


$$ ATP + H_2O= AMP +PP_i $$

[1 ]  Frey, &amp; Arabshahi (1995) give a value of -45.6 kJ mol-1 (-10.9 kcal mol-1).
[2] Dixon et al  (2000) give a value of  -48.5 kJ mol-1 (-11.6 kcal mol-1).
[3] Schuegraf et al (1960)  give a value of  -43 kJ mol-1 (-10.3 kcal mol-1).
[4 ] Calculation from the tables supplied by Alberty (2000) gives a value (25oC, pH 7, ionic strength of 0.1) of -50.2 kJ mol-1 (-12.0 kcal mol-1)



$\Delta G^{o'}$ for the following reaction is about -36 kJ mol-1 (-12 kcal mol-1)

$$ ATP + H_2O= ADP +P_i    $$

[1] Frey, &amp; Arabshahi (1995) give a value of -32.6 kJ mol-1 (-7.8 kcal mol-1).
[2] Rosing &amp; Slater, 1972 give a value of -31.5 kJ mol-1 (-7.53 kcal mol-1).
[3] Calculation from the tables supplied by Alberty (2000) gives a value (25oC, pH 7, ionic strength of 0.1 ) of -36.6 kJ mol-1 (-8.8 kcal mol-1)



$\Delta G^{o'}$ for the following reaction is about -34 kJ mol-1 (-8.1 kcal mol-1)

$$ ADP + H_2O= AMP +P_i $$

[1] Calculation from the tables supplied by Alberty (2000) gives a value (25oC, pH 7, ionic strength of 0.1) of -34.04 kJ mol-1 (-8.13 kcal mol-1)



$\Delta G^{o'}$ for the following reaction is about -71, kJ mol-1 (-16.9 kcal mol-1)

$$ ATP + 2 H_2O = AMP + P_i  + P_i$$

[1] Calculation from the tables supplied by Alberty (2000) gives a value (25oC, pH 7, ionic strength of 0.1) of -70.68 kJ mol-1 (-16.9 kcal mol-1)


$\Delta G^{o'}$ for the following reaction is about -13.7 kJ mol-1 (-3.3 kcal mol-1)
$$ AMP+ H_2O  =  Adenosine  +P_i $$

[1] Calculation from the tables supplied by Alberty (2000) gives a value (25oC, pH 7, ionic strength of 0.1) of -13.74 kJ mol-1 (-3.28 kcal mol-1)



$\Delta G^{o'}$ for the following reaction is about -20.5 kJ mol-1 (-4.9 kcal mol-1)

$$ PP_i + H_2O= P_i +P_i $$

[1] Frey, &amp; Arabshahi (1995) give a value of -19.24 kJ mol-1 (-4.6 kcal mol-1).
[2] Calculation from the tables supplied by Alberty (2000) gives a value (25oC, pH 7, ionic strength of 0.1) of -20.5kJ mol-1 (-4.9 kcal mol-1)