Vague and unclear, on both counts, I’m afraid. You’ll have to ask the DM and/or make your own choice if you are the DM.

In detail, dispel magic and antimagic field both have the effect of temporarily suppressing magic. And there are arguments for and against that working, as well as arguments for and against the sovereign glue’s adhesion being restored after the suppression ends.

Suppression Works

The argument for suppression working is that sovereign glue doesn’t say anything explicitly about it not working, and sovereign glue’s ability to join two surfaces is clearly magical. When suppressed, that adhesion goes away, and the two can be separated.

Note that found or bought sovereign glue has caster level 20th, making it rather difficult to dispel.

Suppression Doesn’t Work

Sovereign glue says this:

If the glue is allowed to set, then attempting to separate the two bonded objects has no effect, except when universal solvent is applied to the bond.

This line notes a single, solitary exception to the blanket statement that the two bonded objects cannot be separated, and that is universal solvent. Since neither dispel magic nor antimagic field is universal solvent, their effects cannot allow the two bonded objects to be separated.

Basically, this is a question of which statement has priority: that magic-suppression stops magical effects from working, or that sovereign glue can be bested only by universal solvent. It’s not clear to me that either statement is officially more-primary than the other.

Adhesion Resumes when Suppression Ends

If we assume that sovereign glue can be suppressed, we then have to determine what happens when it stops being suppressed.

The default behavior for magic items is to just resume their normal function. In the case of sovereign glue, bonding two objects.

Even if we allow that, there are still questions:

• does the sovereign glue have to set again?
• does the sovereign glue only work with the objects it originally bonded to, or can it be applied to some other objects while suppressed and then allowed to bond those?
• if the sovereign glue is not between two surfaces when suppression ends, does it just become useless, as if the objects-to-be-bonded were separated during setting? or does it now become eligible to bond to whatever is placed on it (allowing for set, if necessary)?

The rules do not have answers to these questions.

Adhesion Doesn’t Resume when Suppression Ends

This could arguably be the case simply because sovereign glue is very much a one-shot deal. Certainly avoids a lot of questions, but barring some explicit statement about it, it seems rather contrary to the norms of magic suppression.

Your question is indirectly addressed by these tweets from Jeremy Crawford:

As DM, I'd rule that you can't control a delayed blast fireball while inside an antimagic field. ... You could regain control when neither you nor the bead was in the antimagic field.

Note that he's assumed the Delayed Blast Fireball spell doesn't get suppressed just because the caster is inside an Antimagic Field; however the intention (the rules are silent on this) is that you can't control a spell while you're in the antimagic field or while the spell is suppressed.