Learn Danish: Min mor bliver overbeskyttende når jeg rejser. - My mother becomes overprotective when I travel.

You would place it right before the adjective it modifies. The sentence becomes Min mor bliver lige lovlig overbeskyttende når jeg rejser (My mother gets a bit too overprotective when I travel). It adds a softened, conversational "a bit too" to the description.

Why doesn't overbeskyttende get an -e or -t ending to match the noun, like most other adjectives?

Words ending in -ende are present participles (like English words ending in "-ing"). When used as adjectives, they never change their endings to match the gender or number of the noun they describe. It stays exactly the same whether describing min mor (singular) or mine forældre (plural).

Could I use er instead of bliver here?

Yes, but it changes the meaning slightly. Using bliver (becomes/gets) emphasizes the change in her behavior triggered by your traveling. If you used er (is), it would just state a static fact about how she acts during that time, losing the sense of her getting that way.

Why use når for "when" here instead of da?

Når is used for things that happen in the present or future, as well as for repeated actions (like "whenever"). Since the sentence uses the present tense (rejser) to describe a recurring event, når is the correct choice. Da is strictly used for a single, specific event in the past.