password policy

the easiest way is to use the generator as normal and validate the PW, if it fails, generate a new one, until the validation succeeds.
From you initial set, it seems that only upper and lowercase characters are possible. Add numbers and special characters as well to the string.

I rather have a script that generates the 10 digit code with the validation above.

A lot of scripts do it the way I described earlier, as the position of special characters, numbers, upper and lower case is also random.
But you can put the validation into your generator:
Check, that it contains at least 1 upper case, at least 3 lower case, 2 numbers and 1 special char after you generated a random 10 char code. If it does not validate, start from scratch.

To get a higher chance of generating it with the correct parts, generate a first random number between 0 and 1. If it is below 0.3, take a lower case, if it is between 0.3 and 0.4 take an upper case, between 0.4 and 0.5 take special char, between 0.5 and 0.7 a number and in the remaining case take any char from all possible chars.

Yeah .. I was asking for help with the actual script. I don't know VBscript  :$  and unfortunately learning will take time I don't have at the moment.

Please try this.

Function generatePassword(passwordLength)
    Dim sDefaultChars
    Dim iCounter
    Dim sMyPassword
    Dim iPickedChar
    Dim iDefaultCharactersLength
    Dim iPasswordLength
    Dim UC_Count, LC_Count, Num_Count, Special_Count
    Dim TempPWD
    Dim boolAddit
    Static oRE
    Dim oMatches
    
    If passwordLength < 7 Then  '7 is min pwd length
        Error 5000
        Exit Function
    End If
    
    If IsEmpty(oRE) Then
        ReDim oRE(3)
        Set oRE(0) = CreateObject("vbscript.regexp")
        oRE(0).Global = True
        oRE(0).Pattern = "[A-Z]"
        Set oRE(1) = CreateObject("vbscript.regexp")
        oRE(1).Global = True
        oRE(1).Pattern = "[a-z]"
        Set oRE(2) = CreateObject("vbscript.regexp")
        oRE(2).Global = True
        oRE(2).Pattern = "[0-9]"
        Set oRE(3) = CreateObject("vbscript.regexp")
        oRE(3).Global = True
        oRE(3).Pattern = "[~!@#$%^+-]"
    End If

    sDefaultChars = "abcdefghijklmnopqrstuvxyzABCDEFGHIJKLMNOPQRSTUVXYZ0123456789~!@#$%^+-"
    iPasswordLength = passwordLength
    iDefaultCharactersLength = Len(sDefaultChars)

    Randomize 'initialize the random number generator

    Do
        'Next pick a character from the candidate list
        iPickedChar = Int((iDefaultCharactersLength * Rnd) + 1)
        TempPWD = sMyPassword & Mid(sDefaultChars, iPickedChar, 1)
        Set oMatches = oRE(0).Execute(TempPWD)
        UC_Count = oMatches.Count
        Set oMatches = oRE(1).Execute(TempPWD)
        LC_Count = oMatches.Count
        Set oMatches = oRE(2).Execute(TempPWD)
        Num_Count = oMatches.Count
        Set oMatches = oRE(3).Execute(TempPWD)
        Special_Count = oMatches.Count
        
        boolAddit = ((UC_Count <= 1) And (LC_Count <= 3) And (Num_Count <= 2) And (Special_Count <= 1))
        
        If Len(sMyPassword) < 7 Then
            If boolAddit Then
                sMyPassword = TempPWD
            End If
        Else
            sMyPassword = TempPWD
        End If
        
    Loop Until Len(sMyPassword) = iPasswordLength

    generatePassword = sMyPassword
End Function

Select allOpen in new window

Note: There are some weaknesses in the VB PRNG that I outlined in this article.
https://www.experts-exchange.com/articles/11114/An-Examination-of-Visual-Basic's-Random-Number-Generation.html

=================
The above solution probably isn't the most efficient, but I started with your code.  If starting from scratch, I probably would select random elements from each of the categories until I reached each of the category (min character) limit, continuing to pick random items until the desired password length had been met.  Then I would shuffle the items into the new password string.

:)