H1B & H4 renewal in process, can we travel?

i am applying for H1 extension for myself & H4 extension for my wife next week.
While the H4 extension is in processing, can my wife travel outside the US? Would that in any way hurt my H1 & her H4 extension?

Also, not just her, can i also travel while the H1 extension is in process? or when is it safe to travel? Please advice

Travelling while extension of stay application is pending isn’t really an issue. However you need to be careful about the reentry timing and the USCIS last action rule.

A common scenario is a person on an H-1B/H-4 visa who files for an extension of status and wants to travel while the extension is pending. If he/she applies for an extension of H-1B/H-4 and then leaves the U.S., the extension may be adjudicated while the person is outside the United States. If this happens the person would need to get a copy of the H-1B/H-4 approval and get a new H-1B/H-4 visa stamp at a Consulate before re-entering. If you re-entered the U.S. on old H-1B/H-4 visa the border officials would stamp your passport only up to the end date of the old H-1B visa. The extension granted while you were traveling would essentially be erased, as the last action you took was entering the country on the old H-1B/H-4 visa and you would be issued a new I-94 with a shorter date.

Best way to do this is travel after the approval of any EOS application and carry the approval notice with you. If your visa is still valid at the time of reentry, you can show the new I797 and the CBP will issue I94 based on your new I797. Otherwise you have to get the visa stamping done based on your new I797 and enter back to the US.

For more details refer the below.

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